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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.

Worth noting, the linkage is Amanda

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