[Mac Cat]

It's a 1917 DWM LP.08, pretty much what you thought.
That was a year of very high production, because WW-1 was going on.

The barrel is numbered to the frame, which is a good thing.
The finish is in poor condition, with a lot of pitting and corrosion.
The serial number on the left side of the receiver is almost obscured.
I don't see any serial number ("91") on the side plate.

The grips appear to be in good condition. They may be numbered to the gun.
(Be careful removing the grips. Push out the right one first from the empty magazine well. Then the left one.)

I can't make out small part numbers that should be on the side plate and other parts.
The middle toggle has the correct number "91", but the ejector looks like it's numbered "04".
You will want to remove the receiver and look at the firing pin and hold-open for partial serial numbers, too (ie "91").

There is about 20% of the straw color remaining on the trigger, safety lever and takedown.
A lot of lugers look this way after being stored in poor conditions (water or even salt water), particularly on one side.

Hopefully water didn't damage the inside of the barrel.

The magazine looks like the right type, wrapped metal with wood bottom.