The quaternary boronitride superconductor La3Ni2B2N3-d (Tc~12-14 K) has a layered structure where LaN-LaN-LaN triple layer blocks alternate with NiB layers. These NiB sheets are isostructural with NiB layers in the borocarbide superconductor LuNi2B2C which exhibits various features of unconventional superconductivity. Our aim is to perform a µSR study of the temperature dependent penetration depth of La3Ni2B2N3 and to compare these (very first) measurements of lambda(T) with our thermodynamic estimates of lambda in terms of simple Ginzburg-Landau relations suggesting lambda(0)~ 210 nm based on Bc(0)= 161 mT, Bc1(0)~13 mT, and Bc2(0)~7.5 T. Interesting aspects are possible spatial anisotropies of the superfluid density at finite applied field in this layered boronitride superconductor with significant anisotropy of the Fermi velocity as well as possible field dependence of lambda(T).