  We report on the observation of a conspicuous loss in an ultracold mixture of
$^{7}$Li and $^{88}$Sr atoms confined in a far-off-resonance optical dipole
trap. We attribute the trap loss to the three-body inelastic Li-Sr-Sr collision
and extract the corresponding three-body recombination coefficient $K_3$ at
$T\sim 18.5,45,70,600$ $\mu K$. The measured three-body recombination
coefficient is about two to three orders of magnitude larger than the typical
values convenient for realizing quantum degenerate gases. It also indicates a
potentially large $s$-wave scattering length between the bosonic $^{7}$Li and
$^{88}$Sr atoms, and essentially rules out the prospect of realizing $^7$Li and
$^{88}$Sr mixtures of high phase space density.
