Can a poor battery make a car run badly?
 

Had to put my lights on today as the weather was awful. I had a problem yesterday where the car "spluttered" and it happened again today. Bear in mind I was towing on both occasions and today it stopped when I turned the sidelights off.

I was told it could be lambda sensor, but this was before realising it stopped with the sidelights off. Do you think thats a coinsedence and the lambda is knackered, or can the battery be on its way out?

Once the engine is running the alternator will supply the electrical needs. You should see around 14.5 v across the battery with the engine running following a start. Anything much less could put the alternator under suspicion.
JohnD