We report muon-spin-rotation (μSR) measurements of the in-plane magnetic penetration depth (λab) in polycrystalline Ca- and La-doped YBa2Cu4O8 superconductors with Tc ranging from 72 to 88 K. In all samples the temperature dependence of the μSR depolarization rate σ(T)∝1/λab2(T) is linear below ∼25 K. This is similar to what was observed in recent μSR and surface impedance experiments on YBa2Cu3O7-δ single crystals. The low-temperature behavior of σ(T)/σ(0)=λab2(0)/λab2(T) shows practically no dependence on doping when plotted versus t=T/Tc. This observation puts important constraints on models proposed to explain the linear temperature dependence of λab in cuprate superconductors at low temperatures.