How to dissolve lumps on lower eyelid after fat transfer without a surgery?

Fat in eyelids cannot be sucked out or dissolved usually but it may surgically removed under careful direct visualization. Sometimes lower blepharoplasty may be an option. Another option may be filler injection around the fat to camouflage it. Consultation is required.

In my 40 years experience I have never found any other way of removing it besides surgery. Cortisone injections often makes it worse.  See a very experienced eyelid  surgeon for an examination and an evaluation. 

I concur with my colleagues except I have personally seen good results with 5 FU injections although this is an off label use (not approved use by the FDA)  of an anti cancer drug.  It has been demonstrated to be safe to use around the eyes. Steroids around the eyes can be fraught with unwanted side effects  I would also recommend massage of these lumps.  It may or may not require surgery.  I would revisit your doctor with your concerns

There is no realistic way of getting rid of fat in your lower eyelids without surgical intervention.
This area is prone to leaving bumps and undesirable outcomes for a fat transfer.
Direct excision is the only real solution in my opinion.
Some doctors will recommend anti-inflammatory steroid injections.
Steroids can cause fat atrophy as a rare undesirable side effects.
This is very unpredictable and fairly rare.
Relying on the side affects to precisely remove that is in my opinion a poor idea.
If someone develops fat atrophy from stared injections and can easily over a shoot in hollow out areas.
Unfortunately online reputation can be easily manipulated by shrewd marketing teams.
The best doctors I know have a little online presence, no social media and some don't even have websites.
I am perplexed when a Doctor Who is recently finished their training and is 60+ reviews when world-class doctors who have been in practice for most of their career and have fewer than 10 reviews.
It can be very difficult to correct undesirable outcomes from facial fat transfer.
In some areas the best action liposuction is possible but this may not be realistic possibility for the lower eyelid area
Best,
Mats Hagstrom M.D.