Is It Normal That I Still Have Hard Lumps on my Lips More Than 1 Month After Injection? (photo)

The asymmetry and change in appearance of your lips is apparent.   Not sure about the lumps, but it is likely the filler material.  If you are unhappy with the result and it is indeed hyaluronic acid, the best initial approach in my opinion is massaging lumps to redistribute the product.

If this doesn't work, hyaluronidase (Vitrace) injection(s) will immediately cause resorption of the filler, and return to your pre-injection appearance.  If you just want certain areas softened, very low dose localized hyaluronidase followed by massage can be tried.

Hi there! Thanks for your query.
I wouldn’t typically expect there to still be lumps present 5 weeks after treatment. I would suggest booking a follow up appointment with your practitioner to discuss the possibility of correction or having the product dissolved.
Hope this helps!
Dr Rupert

Lip filler bumps is fairly common after filler.  The bumps can occur early on and many settle down.  Although massage after filler is considered a mainstay, beware that massage can drive the filler into another location if done too early.  
Reasons for bumps after filler:
Technique- Filler may have been used too superficially or wrong type of filler
Mouth movements- In some patients their movements can promote the accumulation of bumps and an alternative technique can be advocated.
Treating lip filler bumps:
Observation +/- massage-  Should be done for almost all lip filler bumps for 2 weeks.  For our patients we usually advocated massage after 48-72 hours to let the filler settle into place.
Reversal- A reversal agent can be used such as Vitrase to dissolve the filler if there is a large obvious persistent bump
Additional filler- An expert filler injector can used improved technique to mask the lip bumps.
The application of lip filler is very technical and should be done by an expert injector.