  We report measurements of the oxygen isotope effect (OIE) on the in-plane
penetration depth \lambda_{ab}(0) in underdoped La_{2-x}Sr_{x}CuO_{4} single
crystals. A highly sensitive magnetic torque sensor with a resolution of \Delta
\tau ~ 10^{-12} Nm was used for the magnetic measurements on microcrystals with
a mass of ~ 10 microg. The OIE on \lambda_{ab}^{-2}(0) is found to be -10(2)%
for x = 0.080 and -8(1)% for x = 0.086. It arises mainly from the oxygen mass
dependence of the in-plane effective mass m_{ab}*. The present results suggest
that lattice vibrations are important for the occurrence of high temperature
superconductivity.
