The aim of this paper is to extend and complete the recent work by Graef et al. (J. Appl. Anal. Comput., 2021) analyzing the asymptotic properties of solutions to third-order linear delay differential equations. Most importantly, the authors tackle a particularly challenging problem of obtaining lower estimates for Kneser-type solutions. This allows improvement of existing conditions for the nonexistence of such solutions. As a result, a new criterion for oscillation of all solutions of the equation studied is established.