  Motivated by recent experiments, which demonstrated lasing and cooling of the
electromagnetic field in an electrical resonator coupled to a superconducting
qubit, we study the phase coherence and diffusion of the system in the lasing
state. We also discuss phase locking and synchronization induced by an
additional {\sl ac} driving of the resonator. We extend earlier work to account
for the strong qubit-resonator coupling and to include the effects of
low-frequency qubit's noise. We show that the strong coupling may lead to a
double peak structure of the spectrum, while the shape and width are determined
to the low-frequency noise.
