  We report the results of muon spin rotation and relaxation ($\rm \mu$SR)
measurements on the recently discovered layered Cu-based superconducting
material La$_{2}($Cu$_{1-x}$Ni$_{x}$)$_{5}$As$_{3}$O$_{2}$ ($x =$ 0.40, 0.45).
Transverse-field $\rm \mu$SR experiments on both samples show that the
temperature dependence of superfluid density is best described by a two-band
model. The absolute values of zero-temperature magnetic penetration depth
$\lambda_{\rm ab}(0)$ were found to be 427(1.7) nm and 422(1.5) nm for $x =$
0.40 and 0.45, respectively. Both compounds are located between the
unconventional and the standard BCS superconductors in the Uemura plot. No
evidence of time-reversal symmetry (TRS) breaking in the superconducting state
is suggested by zero-field $\rm \mu$SR measurements.
