Strainstress:
The vessel is 7.5' dia. and about 17' tall, and weighs 5kips. But, we don’t know anything about the head shape, the location and orientation of the lifting lugs, or the design of the legs or feet. Maybe a sketch would be in order. Can you roll the vessel at all to orient the lifting lugs. Obviously, it is best if you lift in the plane of a couple lifting lugs, not perpendicular to their plane (out of plane bending and prying). In any case, you have to take a look at their stresses during this lift, and what they might do to the head and the lugs. That load will be about 2.5k depending upon the tank C.G. location. The same load will be applied to one or two feet, and the question is, can the feet or legs take this lateral load (cantilever loading and end moment at the tank) during the early stages of the lift. I’m not sure how you would lift this differently even if you had two cranes, except that you might be able to lift the feet off the floor during the early stages of the lift, if they are particularly fragile. There are a number of different sling arrangements that you might use, and you probably don’t have some of them. Maybe you could bolt a beam btwn. two lugs and lift from the center of the beam if that helped. You might brace btwn. the legs to stiffen them. Get you Engineering Mechanics (Statics) and Strength of Materials books out and thing through the lift at 20̊ increments. Ask the shop guys, crane operator, how they would do this, and then check the loads and stresses imposed.