  Detecting Majorana fermions in experimental realizations of the Kitaev
honeycomb model is often complicated by non-trivial interactions inherent to
potential spin liquid candidates. In this work, we identify several distinct
thermodynamic signatures of massive, itinerant Majorana fermions within the
well-established analytical paradigm of Landau-Fermi liquid theory. We find a
qualitative and quantitative agreement between the salient features of our
Landau-Majorana liquid theory and the Kitaev spin liquid candidate
Ag$_3$LiIr$_2$O$_6$. Our study presents strong evidence for a Fermi liquid-like
ground state in the fundamental excitations of a honeycomb iridate, and opens
new experimental avenues to detect itinerant Majorana fermions in condensed
matter systems.
