  We measure the interspecies interaction strength between $^7$Li and $^{87}$Rb
atoms through cross-dimensional relaxation of two-element gas mixtures trapped
in a spherical quadrupole magnetic trap. We record the relaxation of an initial
momentum-space anisotropy in a lithium gas when co-trapped with rubidium atoms,
with both species in the $|F=1, m_F = -1\rangle$ hyperfine state. Our
measurements are calibrated by observing cross-dimensional relaxation of a
$^{87}$Rb-only trapped gas. Through Monte Carlo simulations, we compare the
observed relaxation to that expected given the theoretically predicted
energy-dependent differential cross section for $^7$Li-$^{87}$Rb collisions.
The experimentally observed relaxation occurs significantly faster than
predicted theoretically, a deviation that appears incompatible with other
experimental data characterising the $^7$Li-$^{87}$Rb molecular potential.
