Yes and no, the Lich King raised the more POWERFUL DKs, but not all of them were raised by the Lich King as Bolvar and Arthas… if you pay close attention to the dialogue during the raising in the initial Northrend campaign for original DKs it says: “You are a group of chosen DKs, raised by the Lich King himself as his elite troops.” This suggests there are others, but less powerful and raised in higher numbers en masse by the Cult of the Damned, and even the DK page for Wiki confirms it.
There’d just need to be a new starting quest where you’re raised by the Cult of the Damned, like most DKs are. This just seems to be one detail the Allied Race/Pandaren DK starter leaves out, that they were raised by the Cult, not necessarily Bolvar himself, we also see the Death Lord (DK PC) is also capable of this with the Blades of the Fallen Prince and the Legion campaign. It just requires the Lich King/Death Lord to raise DKs above a certain mastery level, like the 4 Horsemen.
Who is being resurrected, the practitioner’s skill, and raw power of both seem to be requirements that increase with quality of the DK raised, for a few nobodies? The Cult should be sufficient.