  The particle lateral distribution function (LDF) of air showers at a given
altitude is sensitive to the mass composition and primary energy of cosmic
rays. Studies of the LDF are difficult to perform due to experimental effects
such as sampling bias, as well as shower-to-shower fluctuations in particle
density. The High Altitude Water Cherenkov (HAWC) observatory, a dense air
shower array located in central Mexico at 4100 m a.s.l., is well-suited to
perform detailed event-by-event studies of the LDF of multi-TeV cosmic-ray
showers. The detector is instrumented with 1,200 photomultipliers (PMTs) in
close-packed water Cherenkov tanks containing a total of 60 ML of water. We
present a study of the LDF of cosmic-ray air showers recorded by HAWC in 2016
with energies between 3 TeV and 300 TeV and zenith angle < 16.7$^{\circ}$. The
data are used to determine the optimal parameterization of the LDF at the HAWC
site. From here the lateral shower age is obtained and its sensitivity to the
cosmic ray mass composition is analyzed.
