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I teach PS via Skype for a large part of my living. I would say both LR and PS. If you are a production photographer you will benefit from the speed and ease built into LR. But for excellence in image quality PS is an absolutely necessity. If you are more of a fine art photographer, I would recommend ACR to PS. If you want a straight forward approach to improving workflow you might consider private lessons Vis Skype. You can find more info on my website: Wildforlight.com
I'm just curious, is it necessary to learn photoshop or do most professionals just get by with lightroom?
It is necessary for professionals. Although LR is getting more and more powerful there are a lot of things critical it can not do, and maybe will never do. But, if you just need to crank through a wedding (or whatever) and make some lightening fast adjustments to a ton of images LR will do that (and more) for you. But if you are looking for fine art quality, PS is absolutely critical.