I think Specific Awoken Skill would prime for a certain Skill itself, not it's stages. So you could make it so it only activates when you use Lazybones Super Saiyan All skill but no other skill, but not tie it to a certain stage. But given that there probably aren't any other skills with this many stages what you could do would be setting it to "52 - Specific Awoken Stage is activated" and then set the values to the stage of UI and MUI.
I think it goes SSJ1,2,3,God, Blue, Blue KK, Blue KK x 10, UI, MUI right? Since it starts counting at 0 the stages for UI and MUI should be 7 and 8(but you can see that for sure if you open the skill with the skill editor) and then set those two to value 1 and 2 of your Super Soul. That would work just fine. Technically that would work for ALL transformations with a stage 7 and 8, but there aren't really many so that might be a workaround.
But if i may ask, why do you want to make it so complicated on yourself? You can open a skill with the skill editor, then in the PUP tab you have the field U_08 that links to a super soul with requirement "1 - Always(Outside Activation)". So if you only want these stages in particular to have this super soul, just make the super soul, set it's activation method to 1- Always(Outside Activation), then put the ID of the Super Soul in the U_08 field of your transformations UI stages. If both stages are supposed to do the same thing you can just use the same Super Soul for both.