Is it possible for a non-invasive procedure like the thread lift to slant a round eye into more of an almond shape?

Thread lift don't work. Canthoplasty alone may not be enough either to create almond eyes in permanent fashion. See following video and website link on details to achieve almond eyes. It all depends on your eye/facial anatomy and goals. Need to see photos and/or evaluation. Skype consult available.

No photos so I can't comment on the likelihood of achieving your goal.  Even lateral canthoplasty has limits on its ability to alter the shape of the eyes.  There is not substitute for a personal consultation.  Consider reposting with a photograph.

Please note: thread lift isn't a non-invasive procedure, it is an invasive procedure.
So no there is no way to get the shape you like whit a "non-invasive" procedure

A thread lift alone will not change the location of the lateral canthus to create a "slanted" appearance. Thread lifts are less invasive than open surgery, however, it would be incorrect to label them as "non-invasive". Best wishes.

You can accomplish a lot with a thread lift, they are great as long as you are after results that last a few months. Reputable, well trained board certified  surgeons do not do that procedure.