This one is interesting. Toward the end of the time that my son drove my 240D, he let it run out of oil, at least it wasn't showing on the stick, and as I recall it took two quarts to fill it up. I didn't see the oil pressure guage with engine running before I replaced the oil. He went off to college a few weeks later.
The car sat outside for some two years and I put it back on the road. It ran fine for awhile, maybe 5 or 6 thousand miles, I'd have to look at the log book to know for sure.
One morning I was screaming down the freeway and it started making lots of noise. I kicked it in neutral and coasted to the break down lane. When I tried to restart it, three cylinders would fire before locking up on the third. There was oil down the left rear of the engine.
I got a parts car and robbed the engine to get it on the road. I have drug my feet about the exploratory surgery to find what was wrong.
I expect that if adding the oil got everything running okay, you should be able to drive it home no problem. It would seem that driving it 'til it gives up would make more sense than doing exploratory surgery on an engine that is running fine.
Let's be sure and share with each other what we ultimately find wrong, and compare notes.
I would drive it home, and enjoy it as long as you can.
'84 Euro 240D, 523K miles
'88 300E 5 Speed
'81 300D Daughter's Car
Over 800,000 miles in