This problem is what ArrayLayouts.jl is designed to solve, but note that view(L,1:n,1:n) does not know from the type information that the view is lower triangular: this means its not clear that ldiv! can be overwrite the result. view(L,Base.OneTo(n),Base.OneTo(n)) is a bit better though not yet supported, but would be easy to add a LowerTrapezoidalLayout for this case so that ArrayLayouts.ldiv!(view(L,Base.OneTo(n),Base.OneTo(n)), Y) works.
I don’t have time to do this myself but happy to walk you through it if you are willing to make a PR.