Should color grading be performed on raw clips, or final sequence?
Grading multiple clips in Premiere is still a bit fiddly compared to something like DaVinci Resolve. If it was only three clips, I would do the grade on one clip, then copy and paste the Lumetri settings onto the other two.
The other option is to use Master Clips in Premiere, where you can apply the correction to the source clips, and then it doesn't matter how many times you chop them up in the edit - they will still have the same correction applied.
The third option is to do use an Adjustment layer over the clips. So you only have to make one Lumetri setting, and apply it to the adjustment layer, then put the layer above all of your clips.