I think this a bit tricky. No oil, no vasoline, cheap, i think this is pretty impossible.
When I startet Penis Enlargement I used a Bodylotion, but I had to buy a new one almost every second week, and all my room was smelling after this lotion.
I used olive oil, but I din't like it too much, so I used vasoline - the bust lube for me.
What are the opportunieties. You could try dry jelqs or you buy a lube that is made for sex, but those are pretty expensive. Maybe you try out a bodylotion, it costs about 3$ a bottle and will last about 2 weeks, depending on how much and how long your girth sessions are.
Greetz