As Mercedes factory tuneup specifies. Check the fuel pressure in the base of the injection pump with a pressure gauge periodically.

Since you rebuilt the lift pump you might remove the spring in the overflow or relief valve on the injection pump and stretch it back to 27millimeters. If it has sagged with age. This overflow valve is actually the fuel pressure regulator in the system.

If you had not rebuilt the lift pump I would have suggested closing off the return line from the injection pump. If no difference was observed you have issues in the system.

The 240d cars are a favorite of mine. I know it is safe to have 19 pounds of fuel pressure. The only way you can really do this is with a cheap 0-30 pound liquid dampened pressure gauge from harbor freight and the fittings to use it for the test. Should still be under twenty dollars for it all.

Checking that pressure say every two years will catch things that are or will cause fuel supply issues down the road as well. It is fairly easy to tune it to 19 pounds pressure. All 240d owners will appreciate the slight power gain. Plus usually the quieter idle. The most important issue is you learn about the fuel supply system in the process.

Your start up issues are usually the knob on the dash that controls the initial idle of the engine may be in the wrong position. It can be other things as well but it would be wrong not to mention that.