Will tight spanx work instead of the compression garment given by the doctor post-tumescent Lipo?

The compression garment should be tight enough so that you feel like you have something on, but not so tight that it hurts.  It should be smooth and even with no ribs bones or seems that leave indentations in the skin.  If you are swelling then the garment is either too loose or you are doing too much.  You might need a lighter garment to sleep in and a tighter garment for the daytime.  The garment should extend beyond the borders of the treated areas in every direction.

compression garments are tighter than spanx, the first 4 weeks after surgery are  very important to have the right compression to avoid any fluid collection. 

If your compression garment is not very tight, ask your surgeon for a smaller one. The surgical compression garments are designed to apply certain and consistent amount of pressure over the treated areas. Most Spanx garments apply less pressure. Ask your surgeon when you can switch to Spanx.

I think that you need to talk to your surgeon about the preferred garment to wear.  Usually compression garments are tighter than a spanx.