There are indications of this.
Both have rich ancestors.
Coincidence, likely to give the MC and Jill a mirrored storyline of the MC's parents and nothing more than that.
The whole overprotective nature of Bella and Jill.
Could be that Bella was friends with Jill's sister and thus has taken it upon herself to look after Jill in memory of Jill's sister.
If Jill's sister has been dead for years, why can't she talk about it? Was it so traumatic? Doesn't she even know how her sister died?
The death of a close relative is always traumatic, so it could very easily be that Jill simply has trouble talking about it because it still affects her deeply. This is not an unusual trait in a person and it is likely due to the nature and circumstances surrounding her death of which Jill will be very much aware.
It was also not specified by DPC how old little Jill was when her sister died. How old Lynette was when she died.
Mathematically it is possible that Jill is the aunt of MC.
Lynette died during childbirth. This was said in the game's intro.
Jill tells the MC on their date in Ep 4 about her memories of her sister, but Jill is only 2 years older than the MC and she couldn't possibly have such strong memories of her sister from that young an age. Plus, Lynette ran away from her family to be with Neil when she was 18, so even if Jill could remember things from when she was 2, she would have had to have been born before Lynette ran away but that doesn't work because there's only 2 years between Jill and the MC and the MC was born
after Lynette ran off to be with Neil.
So, both mathematically and narratively, Lynette is
NOT Jill's sister.