PS and Lightroom are fundamentally different. Lightroom keeps the Raw file and a stores all of your edits to it, in the the catalogue - the file won't get bigger.
Raw files are very compact, but turn them into tiffs and they get bigger, it's because the data is stored differently.
Apparently compression doesn't work well on 16 bit files they can even get bigger if you use compression. I just tried a random 16 bit file saved as a tif, then with LZW and Zip compression. They were 115, 106 and 104 MB respectively. if I convert to 8 bit the file sizes become 57.6/30.7/27.6 MB repectively. You can see that compression nearly halves the size of the 8 bit file but barely makes a dent in the 16 bit file. Another 16 bit 136 MB tif file started off as a 17MB 20MP Raw file when saved unchanged as a tiff. That's just how much space it takes to store all the data in that form.
Now the next question to ask is do you need 16 bit tiffs stored? IMO, you don't 16 bits main advantage is for headroom when editing it keeps gradients smoother so you don't posterize things like the sky or water when you stretch data. Once you've edited it and providing you don't edit it any more 99.99% of the time you won't notice the difference between an 8 bit and a 16 bit file. I store all my edited files as 8bit LZW compressed tifs. If you store a layered tiff you can always change the file back to 16 bit and paste a new 16 bit converted RAW image in, provided you haven't done any cloning on it.
Lightroom is getting better but it can't do what PS can do with layers and it doesn't have a levels option, I've never used Lightroom for those reasons. Also unless things have changed as I understand it cloning things like backscatter out of your image is way easier in PS.
I would suggest use PS when you need it and store the results as 8 bit. OR: storage is pretty cheap these days bite the bullet and get bigger hard drives.