The actress -- who was up for Best Actress last night, but lost to Emma Stone -- stepped out for Apple's Oscars after-party at the Sunset Tower Sunday evening ... and she was hobnobbing with Apple's CEO, even stepping in to take some photos with him.

Before the cameras could fully snap away, though ... her touch-up crew had to constantly come over and adjust things on her -- which left Timbo awkwardly waiting right by her side.

Check out the video, obtained by TMZ ... TC is trying to figure out what to do with himself as Lily's team keeps doing its work ... moving her dress around, fixing her hair, etc. You can tell he's a bit of an afterthought here -- and he's just there to make her look good!

Tim was notably unbothered ... he just smiled and stood to the side of the chaos. Eventually, Tim and Lily were able to pose for a series of pics -- so, mission accomplished.

Understandable that Lily would warrant this type of attention on Oscars night -- she was one of the front-runners during the ceremony ... but even after losing out to Emma, it looks like people still were hyper-focused on her and wanting to chat her up. Tim ... not so much.

A lot of folks feel like LG actually got snubbed out of a statuette ... but we'll leave that be.

Everyone from "Killers of the Flower Moon" left empty-handed, in fact, but hey ... at least they have each other -- not to mention a bunch of handlers who'll jump in at a moment's notice.