Volume and surface registrations are not related, because surface resampling primarily depends on spherical coordinates, not anatomical. "fs_LR" is only a surface registration template. As long as the volume to surface mapping used surfaces with the same volume registration as the input volume data, you are fine for that step. You will need a surface registration such as MSMAll, MSMSulc, or freesurfer (freesurfer needs an extra step) in order to correctly get your data into alignment with the fs_LR surface template. However, if you want to use the standard 91282 grayordinate cifti space for your data, then you will also need to resample the subcortical part of your volume data to MNI using nonlinear volume registration.
Note that we strongly recommend using the individual's own surfaces to map their volume data to the surface for analysis. There are methods that use group average surfaces for mapping purely for visualization, but such methods are not precise, and will substantially impact analysis of the resulting surface data.
Tim