Could hydroxyurea therapy cause leukemia and/or lymphoma among patients?

Possibly: The agent is considered mutagenic and although the risk is low, it is a real one.

Not likely: The agent has been used safely at varying doses for decades. Typically a very very well tolerated agent, though rarely some patients have ulcerating skin lesions from it. It can cause very low blood counts, but in terms of actually damaging the cells to cause leukemia by itself most people do not feel this is the case.