Can I get lipo without worrying about the mesh getting burned or melted?

Hey there, thank you so much for submitting your question. 
The most important thing to make sure is that your surgeon is aware of your history of hernia repairs and that he/she examines you to make sure you do not have any recurrence etc. 
Regarding burns from liposuction: it depends on the type of liposuction. I typically use SAFE liposuction or standard suction assist liposuction in my practice in order to avoid the risk of thermal injury associated with laser lipo and ultrasound assisted liposuction. Additionally, according to the literature there is minimal if any benefit at all with those forms of liposuction. 
The mesh should not really be at any risk anyway from any of the forms of liposuction but obviously make sure your surgeon is aware! Thank you for your question and I hope this answers your question. 

KrystalI appreciate your concern, however skin burn after liposuction is an entirely different entity. There should not be a contraindication to your undergoing liposuction even though there is mesh present, however it is extremely important to notify your plastic surgeon about this situation so the mesh can be avoided doing surgery. Be certain to consult with a board-certified plastic surgeon. Good luck.

sometimes mesh is placed inside the abdomen to repair certain hernias so it's not necessarily going to be in the way in regards to liposuction but sometimes if the  mesh is on top of the muscles in which case it could be in the area where the liposuction is taking place. 
 Liposuction does not generate heat and does not cause burns. 
 The burn type injuries that you have seen are more likely ischemic injuries from the destruction of blood vessels below the skin. 
 It's possible that the use of lasers or even ultrasound with VASER can also cause skin injuries.
 While unlikely it's possible that the mesh could become contaminated from a liposuction procedure. Should the mesh become infected it would need to be removed which could potentially cause a fairly serious complication for you.
 Tell your plastic surgeon about your history and if possible get a copy of the operative report from one down hernia was repaired so your plastic surgeon can review exactly how the mesh was placed. 
 Best,
Mats Hagstrom M.D. 

The mesh could be damaged by any liposuction procedure, although that would be very unlikely if done by an experienced surgeon using the tumescent technique.. However adding the laser component to the liposuction may run a higher chance of damage.