It probably is time to rebuild/replace the lift pump.
Most likely the o-ring/check valves in the lift pump have worn out after many years of faithful service, and you are (partly) losing prime as a result.
I believe your lift pump is MB part number 001 091 53 01, Bosch number 0 440 007 014.
Still available new, not to bad a price considering it comes with a new primer pump
You will also need a new fuel pump gasket, MB part number 0000911780.
Edit: You can test for losing prime overnight.
Park uphill and install a fuel line clamp on the rubber fuel feed line just before the lift pump.
If it starts up in the morning without issue, right after you have removed the fuel line clamp, you will have found the cause.
Hope this helps.
