  The total disk gas mass and elemental C, N, O composition of protoplanetary
disks are crucial ingredients for our understanding of planet formation.
Measuring the gas mass is complicated, since H$_2$ cannot be detected in the
cold bulk of the disk and the elemental abundances with respect to hydrogen are
degenerate with gas mass in all disk models. We present new NOEMA observations
of CO, $^{13}$CO, C$^{18}$O and optically thin C$^{17}$O $J$=2-1 lines, and use
additional high angular resolution Atacama Large Millimeter Array millimeter
continuum and CO data to construct a representative model of LkCa 15. The
transitions that constrain the gas mass and carbon abundance most are C$^{17}$O
2-1, N${_2}$H$^+$ 3-2 and HD 1-0. Using these three molecules we find that the
gas mass in the LkCa 15 disk is $M_\mathrm{g}=0.01 ^{+0.01}_{-0.004}
M_{\odot}$, a factor of six lower than estimated before. The carbon abundance
is C/H = ($3 \pm 1.5) \times10^{-5}$, implying a moderate depletion of
elemental carbon by a factor of 3-9. All other analyzed transitions also agree
with these numbers, within a modeling uncertainty of a factor of two. Using the
resolved \ce{C2H} image we find a C/O ratio of $\sim$1, which is consistent
with literature values of H$_2$O depletion in this disk. The lack of severe
carbon depletion in the LkCa 15 disk is consistent with the young age of the
disk, but contrasts with the higher depletions seen in older cold transition
disks. Combining optically thin CO isotopologue lines with N$_2$H$^+$ is
promising to break the degeneracy between gas mass and CO abundance. The
moderate level of depletion for this source with a cold, but young disk,
suggests that long carbon transformation timescales contribute to the
evolutionary trend seen in the level of carbon depletion among disk
populations, rather than evolving temperature effects and presence of dust
traps alone.
