Can he tell lies to his parents in order to increase their good deeds?

The basic principle concerning telling lies is that it is
one of the signs of the hypocrites, because the Prophet (peace and
blessings of Allaah be upon him) said: “The signs of the hypocrite are
three: when he speaks, he lies, when he makes a promise he breaks it, and
when he is entrusted with something he breaks that trust.” Narrated by
al-Bukhaari, 32; Muslim, 89. 

But there are some instances in which Islam permits lying, if
that serves a greater purpose or wards off a greater harm: 

These cases include the following: 

1-When a person is intermediating
in order to bring about reconciliation between two disputing parties.

2-When a man speaks to his wife,
or a wife to her husband, concerning matters that will increase the love
between them.

3-War.

It was narrated from Umm Kulthoom bint ‘Uqbah that she heard
the Messenger of Allaah (peace and blessings of Allaah be upon him)
say: “He is not a liar who brings about reconciliation among people, conveys
good words and says good things.” 

Narrated by al-Bukhaari, 2546; Muslim, 2605 

It was narrated that Asma’ bint Yazeed said: The Messenger of
Allaah (peace and blessings of Allaah be upon him) said: “Lies are not
appropriate except in three cases: when a man speaks to his wife to please
her, telling lies at times of war, and lying in order to bring about
reconciliation between people.” 

Shaykh al-Albaani said: it is hasan. 

What you have mentioned is no excuse for telling lies to your
family. If you are honest with them they will never be deprived of the
reward for spending on you. And you can combine your family’s spending on
you and their giving in charity to the needy by encouraging them to spend
for the sake of Allaah, with no need to tell lies about buying stuff when
you have not done so.  

We ask Allaah to correct your intention and set your affairs
straight, and to reward you greatly for your desire to benefit your family. 

And Allaah knows best.