There is no shortage of pedicabs plying the streets of Lhasa, but they require endless haggling and are only really useful for short trips (around ¥5). At least most are Tibetan owned. Always fix the price before getting in.
Buses (¥1) are frequent on Beijing Donglu, and if you need to get up to western Lhasa this is the cheapest way to do it. That said, route maps are in Chinese only, so if you aren't with your guide it's easiest to just take an inexpensive taxi.