She has been living with a man for several years and she wants to do Hajj then go back to him

Firstly: 

You have to understand that this living together is blatant zina
(fornication or adultery) which is a major sin, concerning which there are
stern warnings which should act as a deterrent and an admonition to any
believing man or woman. These warnings include the following:

1.

The report narrated by al-Bukhaari (1386), according to which the Prophet
(blessings and peace of Allah be upon him) described the punishment of the
fornicators or adulterers, among the things that he saw in his dream when
two angels came to him: “… Then we moved on until we came to an opening like
an oven, the top of which was narrow and the bottom was wide. A fire was lit
beneath it and when it flared up, they (the people in that place) rose up
until they almost came out, then when it subsided they fell back into it. In
it were naked men and women. I said: ‘Who are these?’ They said: ‘Move on,’
so we moved on…” 

According to another report narrated by him (7047): “We moved on until we
came to something like an oven.” He (the narrator) said: I think he said,
“in which there was noise and voices. We looked into it and saw in it naked
men and women. Flames came to them from beneath them, and when those flames
came to them they began to shout. I said to them: ‘Who are these people?’
They said to me: ‘Move on, move on’…” At the end of the hadith it says: “As
for the naked men and women who were in a structure like an oven, they were
the men and women who committed zina.” 

2.

Ibn Khuzaymah and Ibn Hibbaan narrated that Abu Umaamah (may Allah be
pleased with him) said: I heard the Messenger of Allah (blessings and peace
of Allah be upon him) say: ‘Whilst I was sleeping, two men came to me and
took hold of my upper arm. They brought me to a rugged mountain and said:
‘Climb up.’ I said: ‘I cannot.’ They said: ‘We will make it easy for you.’
So I climbed up until, when I reached the top of the mountain, I heard loud
voices. I said: ‘What are these voices?’ They said: ‘These are the howl of
the people of hell.’ Then I was taken further on, and I saw some people who
were hanging by their Achilles tendons, with the sides of their mouths cut
open and streaming with blood. I said: ‘Who are these?’ He said: ‘These are
the people who broke their fast before it was permissible to do so.’” Then
he said: May the Jews and the Christians be doomed. Sulaymaan said: I do not
know whether Abu Umaamah heard it from the Messenger of Allah (blessings and
peace of Allah be upon him) or it was his opinion. “Then he went on, and saw
some people whose bodies were greatly swollen and emitted a foul stench, and
they looked terrible. I said: ‘Who are these?’ He said: ‘These are the slain
disbelievers.’ Then he took me further on, and I saw some people whose
bodies were greatly swollen and emitted a foul stench, as if their stench
was that of latrines. I said: ‘Who are these?’ He said: ‘These are the men
and women who committed zina’…”

This hadith was classed as saheeh by al-Albaani in Saheeh at-Targheeb
wa’t-Tarheeb, no. 2393 

3.

Allah has ordained that the punishment of the zaani (fornicator) who was not
previously married should be one hundred lashes, and the punishment for the
one who was previously married should be stoning to death. Allah, may He be
exalted, says (interpretation of the meaning):

“The woman and the man guilty of illegal sexual intercourse,
flog each of them with a hundred stripes. Let not pity withhold you in their
case, in a punishment prescribed by Allah, if you believe in Allah and the
Last Day. And let a party of the believers witness their punishment”

[an-Noor 24:2]. 

Muslim narrated in his Saheeh (3199) that the Prophet (blessings and
peace of Allah be upon him) said: “In the case of a previously married man
[committing zina with] a previously married woman, (the punishment is) one
hundred lashes and stoning.” 

So
hasten to repent to Allah, may He be exalted, and sever your relationship
with this man, and do not be deceived by the fact that Allah, may He be
exalted, has been giving you respite, for He gives respite but does not
forget, and His punishment, when it comes, is severe and great indeed. He
has given you respite for many years – according to what you say in your
question – and this is because of His forbearance towards His slaves and His
desire that they should be guided, and His rejoicing when they repent. We do
not know, by Allah, how you could have lived for so many years with a man
and interacted with him as if you are married. If at that time you were far
away from Allah and drowning in worldly desires, then perhaps the fact that
you are thinking of Hajj is an indication that you want to come back to
Allah and save yourself from the Fire, for death is ever near and this world
will soon perish, then tomorrow it will be either Paradise or Hell, then
whoever is saved from the Fire and admitted to Paradise has attained
success. We ask Allah to accept your repentance and make you one of its
people. 

Secondly: 

It
is not permissible for you to marry this man unless he declares his Islam
and adheres to Islamic rulings, because it is not permissible for a Muslim
woman to be the wife of a disbeliever. This is a matter on which there is
scholarly consensus, because Allah, may He be exalted, says (interpretation
of the meaning):

“then if you
ascertain that they are true believers, send them not back to the
disbelievers, they are not lawful (wives) for the disbelievers nor are the
disbelievers lawful (husbands) for them”

[al-Mumtahinah 60:10]

“And give not
(your daughters) in marriage to Al-Mushrikoon till they believe (in Allah
Alone) and verily, a believing slave is better than a (free) Mushrik
(idolater, etc.), even though he pleases you. Those (Al-Mushrikoon) invite
you to the Fire, but Allah invites (you) to Paradise and Forgiveness by His
Leave, and makes His Ayat (proofs, evidences, verses, lessons, signs,
revelations, etc.) clear to mankind that they may remember”

[al-Baqarah 2:221]. 

Marriage to a non-Muslim is not regarded as a marriage; rather it is
fornication, sin and an evil deed. 

You should understand that he is a man whom it is prohibited for you to
marry, and you are living with him in an unlawful manner, yet you want to
maintain that. This is darkness upon darkness. Save yourself before it is
too late. 

Now you have two options: 

You can give precedence to Allah, may He be exalted, and seek that which is
with Him of eternal happiness and bliss, and a life of ease; or you can give
precedence to this sinful life with a man who is not permissible for you,
but soon this life will end and you will die and your body will
disintegrate, and you will await the reckoning and recompense, at which time
the wrongdoer will bite on his hands and say:

“ ‘Oh! Would
that I had taken a path with the Messenger (Muhammad (blessings and peace of
Allah be upon him)),

‘Ah! Woe to me! Would that I had never taken so-and-so as a
friend!

‘He indeed led me astray from the Reminder (this Quran) after
it had come to me. And Shaitan (Satan) is ever a deserter to man in the hour
of need!’”

[al-Furqaan 25:27-29]. 

One dip in the fire of Hell is enough to guarantee that one will forget all
the pleasures of this life, no matter how great they were. 

Muslim (2807) narrated that Anas ibn Maalik said: The Messenger of Allah
(blessings and peace of Allah be upon him) said: “The most affluent of the
people in this world, of those who will go to Hell, will be brought on the
Day of Resurrection and dipped once in the Fire. Then it will be said: O son
of Adam, did you ever see anything good? Did you ever have any pleasure? He
will say: No, by Allah, O Lord. Then the most destitute of the people in
this world, of those who will enter Paradise, will be brought and dipped
once in Paradise, and it will be said to him: O son of Adam, did you ever
see anything bad? Did you ever experience any hardship? He will say: No, by
Allah, O Lord. I never saw anything bad and I never experienced any
hardship.” 

Thirdly: 

The most serious thing that may befall the one who persists in sin is that a
seal will be placed on his heart, he will be prevented from repenting and a
bad end will be decreed for him. We ask Allah to keep us safe and sound. 

Some of the sinners delay repentance and procrastinate about the decision to
give up their sin, thinking that they will repent at the end of their lives,
but then they are prevented from doing so, so they die in a state of sin and
they meet Allah in a state of misguidance, and they regret it at a time when
regret is of no benefit. 

So
our advice to you is to come back to Allah and begin to obey Him; humble
yourself before Him and shed tears of repentance and regret. Ask Him and
call upon Him a great deal to accept your repentance, forgive your sin and
pardon your errors, for He, may He be glorified, loves those who repent,
brings close to Him those who ask for forgiveness, and He rejoices over
those who turn back to Him. “Know they not that Allah accepts repentance
from His slaves and takes the Sadaqat (alms, charities) and that Allah Alone
is the One Who forgives and accepts repentance, Most Merciful?” [at-Tawbah
9:104]. 

May Allah protect you from all evil, divert from you all immoral deeds, and
bring you back safely to Him. 

And Allah knows best.