Lugs are theoretically stronger because they brace the joint. In practice, you shouldn't be pushing your frame that hard. If you're getting into the realm where you're looking at joint failure, then you should probably move up to a larger and stronger tubeset.

Lugs can accommodate a custom geometry, you can either hand cast them (no small task) or bend them into shape. The latter's not uncommon, you just put some appropriately-sized pipe into the lug and lever it a few degrees into place.

There's nothing wrong with TIG. It's fast, cheap, and also allows custom geometry. Ask Thylacine on here or look at fabricators like Matt Chester or Mike Flanigan. They make fine quality machines with welded joints.