'Sons of Anarchy' Star Johnny Lewis -- May Have Fathered Love Child with 'Sons' Actress ... Before Murderous Rampage

"Sons of Anarchy" actor Johnny Lewis believed he may have knocked up an actress who appeared on the show a few years before going on a murderous rampage in 2012 ... this according to court docs obtained by TMZ.

Lewis died last September ... after snapping at the Los Feliz home where he had been living -- killing 81-year-old Catherine Davis and dismembering her cat, before falling off the roof of the home and plummeting to his death.

Now, Lewis' family has filed court docs in L.A. County Superior Court in an effort to divide the actor's estate -- which is valued at $41,000 ... kinda low for someone who played a major character on the show for a full 2 seasons.

According to the docs, 28-year-old Lewis did not have a will at the time of his death -- and Johnny's father believes he and his wife should be the sole beneficiaries of the estate.

However, under a section of the court docs which lists possible beneficiaries ... Lewis' father lists Diane Marshall-Green ... an actress who appeared on an episode of "Sons."

Lewis also lists Diane's 3-year-old daughter.

And why? According to Lewis' attorney ... before Johnny died, he believed he may have been the father of Diane's kid ... and even went so far as to seek visitation rights.

But for some reason ... we're told Johnny's dad believes his kid was wrong and he was NOT the father of Diane's daughter.

If the kid turns out to be Johnny's, the child would be entitled to the entirety of Johnny's estate.

We reached out to Diane for comment -- so far, no word back.