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We apply the filtered and graded methods developed in earlier works to find(noncommutative) free group algebras in division rings.  If $L$ is a Lie algebra, we denote by $U(L)$ its universal envelopingalgebra. P. M. Cohn constructed a division ring $\mathfrak{D}_L$ that contains$U(L)$. We denote by $\mathfrak{D}(L)$ the division subring of $\mathfrak{D}_L$generated by $U(L)$.  Let $k$ be a field of characteristic zero and $L$ be a nonabelian Lie$k$-algebra. If either $L$ is residually nilpotent or $U(L)$ is an Ore domain,we show that $\mathfrak{D}(L)$ contains (noncommutative) free group algebras.In those same cases, if $L$ is equipped with an involution, we are able toprove that the free group algebra in $\mathfrak{D}(L)$ can be chosen generatedby symmetric elements in most cases.  Let $G$ be a nonabelian residually torsion-free nilpotent group and $k(G)$ bethe division subring of the Malcev-Neumann series ring generated by the groupalgebra $k[G]$. If $G$ is equipped with an involution, we show that $k(G)$contains a (noncommutative) free group algebra generated by symmetric elements.

Free group algebras in division rings with valuation II