This sentence is ambiguous. "He" could refer to either:

1. **The doctor** was late
2. **The nurse** was late

Grammatically, "he" most naturally refers to the nearest male noun (the doctor), so that's the most likely interpretation. However, the sentence is unclear enough that it could reasonably mean either person was late.

To avoid ambiguity, it would be better to rewrite it as: "The doctor phoned the nurse because the doctor was late" or "The doctor phoned the nurse because the nurse was late."
