Lip fillers are safe while taking just about any medication. The main issue is bruising and swelling which would be much more likely and last longer particularly with aspirin, but also with a blood thinner such as warfarin.
We do fillers all the time in people on warfarin and other blood thinners. This has become common since the same population that needs the fillers are the ones that are also most likely to be on blood thinners, and the number of people on blood thinners has risen. We generally use a blunt needle to reduce the chance of bruising and use bromellin and Anrica to help any bruising that does occur absorb faster.