  We report the effect of a coherent drive on transient lasing in three-level
$\Lambda $ and $\Xi$ configurations ($c\leftrightarrow a\leftrightarrow b$). We
show that the presence of a resonant coherent drive on the $a\leftrightarrow c$
optical transition can yield an order of magnitude enhancement of the output
laser energy on a $a\rightarrow b$ XUV or X-ray transition than with no
coherent drive. We demonstrate the crucial role of coherence $\varrho_{ac}$ for
the laser power enhancement. Contrary to the forward direction (with respect to
the pump), where forward gain can be enhanced for some choice of the drive Rabi
frequency $\Omega_{c}$, coherent drive on the $ac$ transition always suppresses
the backward gain.
