Could a scratched lip two days after lip filler cause an infection?

Any scratch / open wound can become infected but most wounds - in a health person - heal well on their own and topical antibiotics are enough. Rednees, pain, swelling and discharge from the wound are common signs of infection. I don’t think scratch will make you lose the filler.

For an infection to get in from the scratch, it would need to go down to the depth of the filler, which is normally a few millimetres down. Scratches tend not to be that deep. the scratch would produce some swelling and tenderness on the lip. 
My recommendation would be to keep an eye on it, if the swelling starts to get worse or it becomes more painful, more red, more hot then contact your Doctor as there may be an infection developing. The scratch itself can also become infected.
Most likely outcome is that all is fine and it all settles down.