We construct the generalized Lie algebras $\mathfrak{s}\mathfrak{p}(4)$, $\mathfrak{s}\mathfrak{o}(5)$, and $\mathfrak{s}\mathfrak{o}(3,2)$, and derive three kinds of (1+1)-dimensional nonisospectral integrable hierarchies. Moreover, we obtain their Hamiltonian structures. Finally, based on Lie algebras $\mathfrak{s}\mathfrak{p}(4)$, $\mathfrak{s}\mathfrak{o}(5)$, and $\mathfrak{s}\mathfrak{o}(3,2)$, by using the semi-direct sum decomposition of Lie algebras, we construct three kinds of integrable coupling systems associated with these three Lie algebras.