What if the Green Card holder never got his citizenship after 38 years (he was brought here when he was 17) married a citizen in 1978 and his US wife passed away in 1990? (never remarried.)

He was convicted of Domestic Violence (former girlfriend) (felony) 2003 and carries a gun.

Is he deportable?

Can he still get his citizenship?

Will the previous encounters with the law be overlooked because they are more than 3 years old?

Is he deportable?
Depends on the documents.. but in my opinion, likely yes.

Can he still get his citizenship?
50-50... you would need an experienced immigration attorney's help to explain why you should be allowed to live in US and become US citizen.

Will the previous encounters with the law be overlooked because they are more than 3 years old?

No.. You should always be honest with USCIS regarding all:

# Arrests (including those by police, Immigration Officers, and other Federal Agents);
# convictions (even if they have been expunged); and
# crimes you have committed for which you were not arrested or
# convicted.

Even if you have committed a minor crime, USCIS may deny your application if you do not disclose the incident. It is extremely important that you tell them about any arrest even if someone else has advised you that you are not required to do so.