In defensive wars yes but does it make sense to die for my overlord's liege in an offensive war? Were there any cases like this irl? If so it shouldn't be "free" ingame and should cost i.e. increased subject's LD.
The game's concept of a "vassal" is a rather hazy concept. Technically, "vassals of vassals" do not exist in the game. Some subject of subject cases can exist, such as vassals of junior partners, but those are still direct vassals of the person of the sovereign, even if it is a subject of a subject of the "tag." Likewise, there are quasi-subjects who have some protections from a higher "liege" but remain effectively sovereign, such as the Princes of the HRE or tributaries.
What would you even consider a "vassal of a vassal" in real life? The only example I can think off of hand is a native tribe which is loyal to a colonial nation. I can list some nominal examples, such as the American colonies being subject to the English crown, which was technically the junior partner of Scotland until 1707. Likewise, Aragon was technically the senior partner in Spain, making Castile's colonies vassals of a vassal. But in both cases, the game lists that England and Castile as the senior partner for playability reasons.
In classical feudalism, the lords of the realm were required to supply the liege with troops, and that hierarchy worked all the way down to the bottom of the feudal hierarchy. I.e. the king would demand troops from his direct vassals, who are in turn supplied with troops by the next level down, and so on.
By the game's logic, a vassal is effectively a client state, having no agency in terms of foreign relations, except its ability to rebel against its liege. Therefore, a vassal can't be a true overlord in its own right, as it is not even a real state.