Case 1: Player-B attempts to summon a dragon type monster, Player-A responds by activating Solemn Strike: Player-B can not activate Return of the Dragon Lords from their graveyard in response, because this effect only applies to dragon monsters currently controlled. Solemn Strike negates the summon, therefore there is nothing in Player-B’s control to protect.

WINNER = Solemn Strike

Case 2: Player-B activates a dragon monster’s effect on the field, Player-A responds by activating Solemn Strike: Solemn Strike will resolve normally, negating the activated monster’s effect, however when applying the second part of its effect to destroy that monster, at this point Return of the Dragon Lords’ effect can be activated from the graveyard in order to protect the dragon monster from destruction (this is not considered “chained” to Solemn Strike).

WINNER = Return of theDragon Lords

See Solemn Strike vs Return of the Dragon Lords discussion here.

See Unclassified Effects and Chains here.

See Unclassified Effects similar to Continuous Effects here.