-Determine lifting loads, angles, and hardware to be used. For API-650 tanks, there are some requirements in Annex J, revised in the last edition or two.
-Check stresses in the lug itself for bending, tear-out, bearing, etc. For this, the provisions of ASME BTH come in handy.
-Check welding connection to the tank.
-Check stresses in the tank shell due to the lifting. In some cases, the clip design from Bednar's handbook may come in handy, in some cases, this may involve a repad and/or analysis via WRC 107/297 or equivalent means.
I'm not familiar with wine tanks. If they're small enough, a lot of this may be overkill. If you're using pre-fabricated lifting lugs, some of this may be simplified.