Hi, 

Don't bother with cinnamon. It doesn't kill the ants and typically only deters them so, they may just move on to another area for the time being. Ants do not harm the plant whose pot they inhabit (and that peace lily looks to be in great shape).

They are finding their way in the house somehow or if the Peace Lily is new they could have come in with it. Ants like the loose "soil" in potting mix because it's easy to nest in, and should be gone once the current mix is replaced with fresh, if you can get most of the potting mix off. 

Ant colonies depend on queen to keep laying eggs to generate more workers, so if the colony is destroyed and the queen lost or killed, the colony won't keep persisting (the workers are not going to form a colony by themselves). If you can get rid of the bulk of the ants then you're probably getting rid of the queen and most of her already-laid eggs with it.

It would be easiest to repot outside on a mild day (if possible) as to not have to try to contain ants that fall all over the place when the pot is emptied, otherwise maybe try this over a trash can. You don't need to disinfect the pot between emptying and refilling it. You can visit out indoor plant care pages and repotting indoor plants page for more details on care and how to repot. 

You can look for any ant trails coming inside and try bait traps (homemade with a borax sugar mix or store bought) and sealing up any gaps or cracks in the wall/door/windows. 

Emily