= Solution
For dry ascent, $c_pdT=Vdp$ and <hydrostatic pressure> change is $dp/dz=-\rho g=-g/V$, so $\boxed{\Gamma_d=-dT/dz=g/c_p}$. During condensation $dq<0$, and $-Ldq>0$ offsets expansion cooling, making the saturated ascent less steep.
For a saturated parcel with $q=q_s(T,p)$, use $dq=q_TdT+q_pdp$ to obtain
$$
\Gamma_m=\frac{g(1-Lq_p/V)}{c_p+Lq_T}.
$$
With dilute vapor, $q_p\simeq-q_s/p$ and $q_T\simeq Lq_s/(R_vT^2)$, this becomes $\Gamma_d[1+Lq_s/(R_aT)]/[1+L^2q_s/(c_pR_vT^2)]$. In terrestrial conditions the denominator's latent-heating correction dominates. Warming increases saturation humidity strongly, so <latent heat> increasingly compensates expansion cooling and the moist <lapse rate (atmosphere)>[lapse rate] falls. This is a statement about saturated <convective adjustment>, not every instantaneous environmental <temperature> profile.
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