Have you seen a shift in colours from lightroom going to photoshop, or is the shift in colours etc only from PS to the print?
From lightroom itself, it should be possible to switch to PS for editing (for those who want). If you haven't assigned PS as photo editor for lightroom yet, maybe you should do this.
In any case, when you go from lightroom to PS if the colours pace is different, PS would come with the mesage that asks you if you want to convert to the working space. If it doesn't, the colour spsace of lightroom is the same as the colour space you assigned for PS. If it does, allow PS to convert the image colourspace to the PS work space.
Also check if you assigned the correct paper profile for preview purposes. There are plenty of guides on this forum and elsewhere onteh internet so I'mnot gonna go into that.
When you print, make sure that you use print with preview. This allows you additional options to select the correct paper profile etc. Again, there are plenty of instructions around to do this so I won't repeat that either.
In any case, you should be able to get the same print as the image you see in PS. If not, you are probably not using the right colour profiles for printing and preview in PS.