First, be sure that you recognize that you don't have an ASME Section VIII vessel. You have a vessel built to the sister code, the API-ASME Code Unfired Pressure Vessels for Petroleum Liquids and Gasses. So be careful of the allowable stresses that you might use in running calc's.
Looking at the 1951 edition of the API-ASME, paragraph W-529 the meaning of the P, I, L, and A stamping is not clear. It is possible that "I" is short for the "I.T." stamping which would be "impact tested". The other modifiers would be XR for radiographed and SR for stress relieved.
In current code, the "L" would mean that the vessel meets the "lethal service" requirements, but I don't see any indication of "lethal" in the 1951 API-ASME in the index.
