I would suggest you see your injector about this, although it doesn't sound like it's product leaking out. This would be highly improbable, since the holes from the needle are mere pin pricks that close easily. You can also see your doctor.
Restylane and dissolving it
I am sorry that you are having a problem with your injections. I have not heard of a filler "leaking" out in the way that you described so it is impossible for me to give you the exact answer that you are looking for. I can tell you that it sounds like the physician injected Hyaluronidase to dissolve the lumps. It is possible that the Hyaluronidase also dissolved the part of the Restylane that you liked in your lips as well. Please find a board certified dermatologist with experience in facial injections for the best cosmetic results.
The needles used to inject Restylane are tiny and they close almost immediately after the needle is removed. What was used to dissolve your filler was hyaluronidase, which is an enzyme, and also injected with a tiny needle, so those pin pricks closed immediately too. Whatever is on your lips isn't the filler leaking out.
"This answer has been solicited without seeing this patient and cannot
be held as true medical advice, but only opinion. Seek in-person
treatment with a trained medical professional for appropriate care."
It sounds like the physician injected hyaluronidase to dissolve the dermal filler injected in your lips since you were concerned with the lumping. The lumping can generally be massaged and even out in a few weeks. However, if the physician did inject hyaluronidase it dissolves the entire filler as it spreads in the lip-it can not just dissolve a tiny lump. While the filler does not leak out it will dissolve completely. You should call and speak with your physician further.