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Let A be a flexible Lie-admissible algebra over a field of characteristic #2, 3. Let S be a finite-dimensional classical Lie subalgebra of A which is complemented by an ideal R of A-. It is shown that S is a Lie algebra under the multiplication in A and is an ideal of A if and only if S contains a classical Cartan subalgebra H which is nil in A and such that HH C S and [H, R] = 0. In this case, the multiplication between S and R is determined by linear functionals on R which vanish on [R, R]. If A is finite-dimensional and of characteristic 0 then this can be applied to give a condition that a Levi-factor S of A be embedded as an ideal into A and to determine the multiplication between S and the solvable radical of A -.

Embedding of a Lie algebra into Lie-admissible algebras