In the lawsuit, Andrea Ashley -- one of JLo's neighbors -- says she was getting out of her car back in December ... when Smart's boxer named Bear mauled her left arm and hand ... leaving her with broken bones and cuts. She's included photos of her bloodied limb in the suit.
Ashley says, right after the attack ... Casper walked out of JLo's house wearing only pajama bottoms and came over to apologize. That's interesting because Casper and Jennifer had broken up several months before the attack. As we reported ... J.Lo's people told us the dogs were only at her house for a visit with her kids. Apparently, Casper was visiting too.
Ashley says this wasn't the first attack -- Bear also escaped through a hole in JLo's fence and attempted to attack her in April. She says only her gardener saved her from getting mauled that time.
In the docs, Ashley says Casper called her, apologized, and offered to pay all of her medical bills. As for why she's suing Lopez ... Ashley says Jennifer bears some responsibility because the dog is escaping through her fence.
Further, she says Bear has remained at Jennifer's home since Jan. 8 ... and she's afraid he could get out again. Animal Control told us Bear was quarantined at Casper's home since the attack.