Let n be a positive integer, and let $A$ be a strongly commutative differential graded (DG) algebra over a commutative ring $R$. Assume that
(a) $B=A[X_1,¥cdots, X_n]$ is a polynomial extension of $A$, where $X_1,¥cdots,X_n$ are variables of positive degrees; or
(b) $A$ is a divided power DG $R$-algebra and $B=A¥langle X_1, ¥cdots ,X_n ¥rangle$ is a free extension of $A$ obtained by adjunction of variables $X_1, ¥cdots ,X_n$ of positive degrees.
In this paper, we study naive liftability of DG modules along the natural injection $A ¥to B$ using the notions of diagonal ideals and homotopy limits. We prove that if $N$ is a bounded below semifree DG $B$-module such that $Ext_B^i(N, N)=0$ for all $i>0$, then $N$ is naively liftable to $A$. This implies that $N$ is a direct summand of a DG $B$-module that is liftable to $A$. Also, the relation between naive liftability of DG modules and the Auslander-Reiten Conjecture has been described.
