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Let n be a positive integer, and let A be a strongly commutative differential graded (DG) algebra over a commutative ring R. Assume that

• is a polynomial extension of A, where are variables of positive degrees; or
• A is a divided power DG R-algebra and is a free extension of A obtained by adjunction of variables of positive degrees.

In this paper, we study naïve liftability of DG modules along the natural injection using the notions of diagonal ideals and homotopy limits. We prove that if N is a bounded below semifree DG B-module such that for all , then N is naïvely 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 naïve liftability of DG modules and the Auslander-Reiten Conjecture has been described.