There are a few hits if you search this particular forum for 'lifting lug calculation' which may be of help to you.
There is an ASME standard called 'ASME BTH-1 Design of Below-the-Hook Lifting Devices' which provides minimum structural design requirements for below-the-hook lifting devices, such as your lifting lugs. This equations used in this standard bear many similarities to the AISC Steel Construction Manual, as you may have expected.
I believe both Compress and PV Elite have have built-in calculations for lifting lugs as well.
If you are also seeking information regarding any vessel stresses which occur as a result of erection, you may refer to the 'Pressure Vessel Design Manual', by D. Moss.
If you are looking for theory behind the various failure criteria to which a lifting lug would be subjected, it may be found in mechanics and strength of materials books, as they are just structural components. Welds may be studied in machine design books, such as Mechanical Engineering Design, by Shigley, or in a book such as Design of Welded Structures by Blodgett.