4140 is not the material of choice if it is welded to ASTM A36. The assembly is only as strong as the weakest link which is of course the ASTM A36.
4140 is a chrome moly alloy steel with 0.4% carbon. The carbon equivalency is rather high. The preheat temperature is dictated by the base metal that requires the higher preheat, 4140 in this case, and I believe it should be higher than 300 degrees F. I've welded similar thicknesses where the preheat was between 550 and 650 degrees F with an immediate (no cool down) stress relief at 1150 degrees F for one hour.
You did not mention the welding process to be used. Needless to say it must be a low hydrogen process or if you use SMAW, you need to use low hydrogen electrodes that have been baked at a temperature of 600 to 700 degrees F for one hour before use to ensure low moisture content.
Good luck, but at least ask the designer why he is specifying the 4140 for the lifting eye.
Jarcher makes a good point regarding the design and selection of materials.
Best regards - Al