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$_3$.
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