Can you elaborate on what you mean? LCDM hasn't been "tweaked" since \Lambda was established in the 90s (at least, not for large-scale cosmological observations). The current discrepancies are all at the precision level (<10%) rather than a qualitative O(1) difference. An important (but not dispositive) nuance is that LCDM well explains all observations individually; the percent-level tensions arise only between fits to datasets, meaning unknown systematics remain a viable explanation.
The unknown fundamental nature of CDM (as important a problem as it is) seems irrelevant to arguments about LCDM's predictivity (as a cosmological model).