She missed some prayers in the past – what should she do?

It
is not clear from your question whether your aunt missed the prayers because
of a reason such as sleeping, forgetting or being unconscious, etc., or whether
she missed them deliberately, with no valid excuse. Whatever the case, if she
missed them for a reason, she has to make up what she has missed, and also repent
for the delay.

If
she did not have any excuse for missing the prayers, but denied that they are
obligatory, or thought that they did not matter, or was too lazy to do them,
then the correct scholarly view is that if a person who does not pray because
he does not think the prayers are obligatory, or he is too lazy or he thinks
they do not matter, there is no way that he can make up these prayers. There
are deeds which must be done for Allaah at night, and He does not accept them
during the day, and deeds which must be done during the day which He does not
accept at night. (See the book: I want to repent, but…)
The person who deliberately does not pray is a kaafir, if he does not pray at
all; but if he repents and prays, he comes back to Islam, and he does not have
to make up what he has missed, but he is advised to do a lot of naafil prayers.
Islam also wipes out whatever (sins) came before.

 Shaykh
Saalih ibn Fawzaan al-Fawzaan (may Allaah preserve him) was asked the following
question:

 “I
am a Muslim woman, al-hamdu-Lillaah. Not so long ago I did not pray and
I did not know anything about matters of religion. But now, al-hamdu Lillaah,
Allaah has guided me and I have started to pray, fast, read Qur’aan and recite
Tasbeeh. I have completed the Qur’aan for the tenth time. Will Allaah forgive
me for what I have done in the past and what I will do in the future, in secret
and openly in my life? What more can I do so that Allaah will forgive me?” 

The
response was: 

Repentance
wipes out whatever (sins) came before it. So long as you have repented sincerely
– al-hamdu Lillaah – and you are doing the duties enjoined upon you by
Allaah and avoiding what He has forbidden, then Allaah will forgive whatever
came before that repentance. Allaah says (interpretation of the meaning):

“Say:
“O ‘Ibaadi (My slaves) who have transgressed against themselves (by committing
evil deeds and sins)! Despair not of the Mercy of Allaah, verily, Allaah forgives
all sins” [al-Zumar 39:53]
– even shirk, if the person who committed shirk then repents from
it to Allaah, He will accept his repentance. Allaah says (interpretation of
the meaning):

“Say to those who have disbelieved, if they
cease (from disbelief), their past will be forgiven” [al-Anfaal 8:38]. The
Prophet (peace and blessings of Allaah be upon
him) said: “Islam wipes away whatever (sins) came before it, and repentance
wipes away whatever (sins) came before it.” (Narrated
by Ahmad, 4/204). If you have repented sincerely and you do what Allaah
has enjoined upon you and avoid that which He has forbidden, this will be sufficient
in sha Allaah for your past sins to be forgiven, but you must good deeds in
the future, and keep on repenting and obeying the Islamic commandments which
Allaah has enjoined upon you.

 And
Allaah knows best.

.