Since you say pressure vessel I will assume ASME Sec. VIII vessel.
I wouldn't weld the lug to the shell then weld a pad around it. I would weld the pad to the shell then the lug to the pad. The benefit of the pad is to reduce the stress concentrations from the smaller area of the lug exerted on the pressure boundary. Generally the pad thickness should be equal to the shell thickness (but your situation should be evaluated on an idividual basis). The CODE and TEMA have lifting lug designs which give good starting points. The pad needs to be large enough to reduce stresses imposed in the shell.
The weight you should set any lift lug to is the safe working load limit for the lift you are doing. You need to look at all loading cases that the lug may be used for (see ASME UG-22). For a lug to shell these are most importantly weld area req'd, shear and bending stresses, weld stress concentrations,impact loadings, and safety factors of the lug and shell. The geometry of your lug and pressure vessel will affect all of these items and the lift you are trying to make.
I assume you are talking about lifting lugs on horizontal vessels, not the top head lugs on vertical vessels.
There isn't definitive weight about which you need to weld lugs to shell through pad. If you have a large and heavy horizontal vessel and you want to use lugs, not belly sling, you should consider welding the lugs directly to shell.
Trunnions on large vertical vessels are typically welded to shell through repad.
My understanding is similar to one of the post in the thread quoted by bernoullies123.
The load has to transfer from the lug to the pad and then to the shell. If your pad is very big then the pad and the shell may not behave as one unit. Specially if you have bending moments and outward pulling loads.
Moreover the welds at the edge of the pad will be bearing lot of stress as they act as link between the shell and lug.
If you use a cut through method yo should pay more attention to the welding, are you doing full penetration groove welds. As you would have more welding the Stress concentration would also be higher. So, having a small radius on the fillet welds would be helpful here. Even though it is not a repeated loading.
But, it is cheaper to weld the lug to pad and then to shell.
