In LrC, even with a Brush or Gradient with Auto Mask & Range Mask, selecting the 'background' and doing an extreme over-exposure will not get you total 'white', unless you photographed items on a white back-drop.
[This post contains formatting and embedded images that don't appear in email. View the post in your Web browser.]
I agree that PS is a more powerful tool for doing this. But you can usually get quick, good results in LR by using the Adjustment Brush and then setting Exposure through Blacks all the way to the right and Clarity all the way to the left:
If there are any stray splotches that still aren't white, you can use the Spot Removal brush with Clone to get rid of them.