Can I go tanning after Smart Lipo?

Any surgical procedure may interfere with the bodies ability to naturally protect itself from actinic radiation (sun exposure).
There are many theories for this and include difficulties with the bodies response and monitored, initiated and controlled via the nervous system.
As a result, it may be very easy to burn. This has implications for scarring as well as long term development of skin cancer.
Areas of prolonged inflammation may also become hyperpigmented.
If and when you return to sun exposure begin slowly and with extensive sunscreen and protection with a high SPF providing broad spectrum coverage. Consider protective clothing.
In summary, take "babysteps" upon returning to the sun.

Yes, you should avoid tanning for now as your skin is very sensitive and you could possibly cause burns to your skin. I would recommend waiting until the majority of your sensation have come back before attempting any tanning. When you do tan, I recommend covering your scars with zinc oxide or good SPF to help discoloration of the scars.
I usually recommend to my patient not to have direct sunlight exposure to the area for about 3-4 months.
Hope that helps.

Tanning is not a good treatment pre or post lipo. You will lose your skin elasticity and there is also risk of skin cancer. If you are aware of these risks, then you can tan .

The only problem to tanning would be to the entry point incisions from the liposuction.  Cover the scars with sunblock or bandaids. I am not a big fan of tanning because it prematurely ages your skin, but if you so choose have a good time.