If your beam is a 2x6 or 2x8 laid flat, is there any need to calculate Rb, le, and lu since they go into the CL equation but CL=1 if you lay the material flat?
Per NDS, yes, you need to consider the adjustment to design values as shown in table 4.3.1 of NDS. However, 3.3.3.1 indicates that is d <= b, then CL = 1.0. Since Rb and le are used for the CL calc, and we already have CL defined in code, we shouldn't need to consider their calculation. Be aware that Rb is a separate check that should be followed, but if you're installing anything in plank orientation, Rb per 3.3.3.6 should not be an issue.
CL in the NDS is intended to address stability and prevent buckling and/or twisting out of plane due to high loads and a lack of restraint.
Similar to Steel and the Lb that affects section strength (i.e. limit allowable stress to a level below which buckling will not occur). As the LTB provisions in steel note, LTB is not a concern (it doesn't physically happen) when you are bending about the minor (weak) axis. Similar applies here to wood construction. ChorasDen is correct. (Side note, use 'cross' material references with caution, but it's supportive in this circumstance as the buckling is a physical phenomenon that is not specific to a material, the material design provisions change but the concept of preventing buckling remains).