Nigel Lythgoe 's doubling down on his denial of Paula Abdul 's sexual assault allegations despite agreeing to a lawsuit settlement with her.

The TV show producer arrived at LAX this weekend ... and a paparazzo asked him what he feels he needs to do to rebuild his legacy after Adbul accused him of forcibly kissing her and grabbing her genitals. Getty

Lythgoe says he doesn't feel he has to rebuild anything ... saying an untrue allegation was made against him -- and, try as he might to deny it, there's not much else he can do.

Instead, Nigel says he's focused on upcoming projects ... revealing he's producing an upcoming show and a film as well -- though he wouldn't say what either project is about.

All this comes less than a year after Paula settled her lawsuit against Ni

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