CeRh₂As₂ has been receiving considerable attention due to its unusual two-phase superconductivity. The superconducting (SC) phase appears at T_c = 0.35 K in an ordered state (phase I) of the Ce-4f moments, which develops below T₀ = 0.55 K. The microscopic nature of phase I has not been fully established yet. We report a single-crystal study of the effect of La substitution on these low-temperature phases in Ce_1-xLa_xRh₂As₂ up to x = 0.1. The lattice parameters increase monotonically with x, corresponding to an effective negative pressure of approximately —0.3 GPa for x = 0. 1. While the Ce³⁺ local valence state and the non-Fermi-liquid behavior are preserved, the resistivity coherence maximum Tma_x ≈ 45 K in the pristine sample shifts to lower temperatures with increasing x, indicating a suppression of the Kondo energy scale upon lattice expansion. On the other hand, both T_c and T₀ are rapidly suppressed to below 0.1 K for x > 0.05. Notably, such a rapid decrease of T_c under moderate negative pressure is unexpected, but is rather consistent with a substitution-induced disorder effect which leads to strong pair breaking in unconventional superconductors. The observed fragility of phase I under both pressure and disorder may imply its itinerant origin.