Will the veins come back if I lift weights at the gym?

This will largely depend upon how they were treated, not what you do. Compression for 2-3 weeks immediately following treatment offers the best chance of cure. At that point, it all depends upon the veins.If small spider veins were treated with sclerotherapy there is a chance they will come back over the years. In addition, new veins can appear for the same reason the original veins appeared. Surgical removal of large veins is one of the few absolutely permanent solutions. However, small veins may still appear in the treated area.

venous insufficiency at the saphenofemoral junction can worsen with weight lifting - as bearing down to lift or doing  Valsalva maneuver, will increase intraabdominal pressure and force blood to leak from deep veins into superficial veins - hence, venous insufficiency. Topical products containing horse chestnut extract will promote vein health (see link below). 

It depends on, first, what kind of veins you had and, second, what type of treatment you underwent. In general, if the condition responsible for formation of your veins was not cured, they do come back regardless of weight lifting.