3:01 PM PT -- Bieber's legal team claims the singer provided alternative dates to sit down for a depo, but Schwartz's attorneys rushed to file warrant docs before trying to work something out. They also claim Bieber hasn't been personally served the lawsuit.

Justin Bieber skipped a scheduled grilling from lawyers, and decided to make out with Hailey Baldwin instead ... according to his ex-neighbor who now wants Justin arrested.

The Biebs was ordered by a judge to attend a deposition, which was scheduled for June 22, in his infamous and STILL ongoing egging case with former Calabasas neighbor, Jeffrey Schwartz.

Problem is, JB didn't show up. According to new legal docs, Schwartz believes it was because he was in NYC packing on the PDA with Hailey. So now, Schwartz wants the judge to issue a bench warrant for Bieber and fine him $1,000 bucks a day for each day he refuses to sit for the depo.

Schwartz also accuses Bieber of engaging in "obfuscation and delay tactics" and points out he's already skipped out on 5 scheduled depos in the past 2 years. The judge has yet to rule on the warrant.

We broke the story ... Schwartz -- who's being repped by John Carpenter and Brian Kim -- wants big bucks from Bieber from all the emotional distress he and his wife suffered from the 2014 egging and the aftermath.