  We present THz measurements of thin films of mixed-valent YbAl$_3$ and its
structural analogue LuAl$_3$. Combined with traditional Fourier transform
infrared (FTIR) spectroscopy, the extended Drude formalism is utilized to study
the low-frequency transport of these materials. We find that LuAl$_3$
demonstrates conventional Drude transport whereas at low temperatures YbAl$_3$
demonstrates a sharply renormalized Drude peak and a mid-infrared (MIR) peak in
the conductivity, indicative of the formation of a heavy Fermi liquid. In
YbAl$_3$ the extended Drude framework shows a consistency of the scattering
rate with Fermi-liquid behavior below $T < 40$ K and a moderate mass
enhancement. While a $\omega^2$ Fermi liquid-like frequency dependence is not
clearly exhibited, the temperature dependence of the Drude scattering rate and
effective mass is consistent with the formation of a low-temperature moderately
heavy Fermi liquid, albeit one with a smaller mass than observed in single
crystals. The extended Drude analysis also supports a slow crossover between
the Fermi liquid state and the normal state in YbAl$_3$.
