Amanda Bynes and her new boyfriend sure seem to be going strong … the duo was recently spotted on a dinner date at an iconic L.A. spot.

TMZ broke the news in September … that the former actress began seeing a dude by the name of Zachary, who’s a year older than the 39-year-old Amanda — and owns an event and security business.

The couple were snapped last night … loved up, holding hands after dinner at Chateau Marmont.

As we reported … Amanda and Zachary started as friends and decided to take that to the next level — but they’re still taking the new ‘ship slow and steady.

And that makes sense … Amanda has a lot going on right now, we’re told … still focusing on her passions of making art and developing her screenplay.