Correct, we use lifting, ie, we assemble a matrix A where all Dirichlet dof rows and columns are set to the identity row/column. Then L is corrected with lifting, by computing L-= Ag Where g is equal to the Dirichlet bc value at those dofs, zero everywhere else.
Ive posted a reference for lifting at Difference between LUSolver and solve - #2 by dokken
where I Also highlight the benefit of lifting, ie symmetry is preserved.