1955 2 stroke. Fresh fuel. New plugs. Carb and air filter cleaned. Points, condenser, and coils are very old but have no miles. Timing checked (no spark advance on this bike). Spark seems very good. In neutral bike starts and revs good. When I try to accelerate in gear, bike lurches terribly.
Any advice on where to look?
On a bike that old it could really be anything. What model?
Is it lurching because the throttle sticks or because it has a light flywheel?
Odd as it sounds – what condition is the chain in? – Commonly overlooked.
The cycle is a 1955 Adler MB200. The throttle is not sticking. The chain was removed, cleaned, oiled, and reinstalled and properly tensioned. In neutral the bike revs fine. By lurching, I mean that when I accelerate, it feels like the engine totally stops firing for a fraction of a second, then resumes power right away, causing the bike to jolt. This happens every couple of seconds until I get up to about 20-30 MPH, when the jolting stops. I hope that I am explaining it sufficiently.
Those are sweeeeeet bikes! 
Lucky!
You could have an electrical issue. But you are riding a 50 year old air cooled 2 stroke, so it could be anything!! Haha. Sounds like a lose electrical connection to me. Pull every connection, clean them, lube them, and put them back together. And double check every wire for damage.