  Single crystal of Lu$_2$Fe$_3$Si$_5$ was studied with the tunnel-diode
resonator technique in Meissner and mixed states. Temperature dependence of the
superfluid density provides strong evidence for the two-gap superconductivity
with almost equal contributions from each gap of magnitudes
$\Delta_1/k_BT_c=1.86$ and $\Delta_1/k_BT_c=0.54$. In the vortex state, pinning
strength shows unusually strong temperature dependence and is non-monotonic
with the magnetic field (peak effect). The irreversibility line is sharply
defined and is quite distant from the $H_{c2}(T)$, which hints on to enhanced
vortex fluctuations in this two-gap system. Altogether our findings provide
strong electromagnetic - measurements support to the two-gap superconductivity
in Lu$_2$Fe$_3$Si$_5$ previously suggested from specific heat measurements.
