Should I buy the Monster Manual?

If I plan to run Lost Mines of Phandelver, and I bought Lost Mines of Phandelver (in Print and Roll20), and I own the MM in print, is there any benefit to owning the Monster Manual in Roll20 format, to run Lost Mines? I might buy it after Lost Mines, so they still might get  my money a second time, I just want to know if I should get it now because it will do something awesome for my current campaign. Thanks.

For running LMoP? Not really. If you plan to run your own campaign later... maybe, if you don't like having to enter all the monsters in by hand.

The primary benefit of purchasing the MM in roll20 format is the monsters are unlocked in the compendium for quick reference and come with pre-statted sheets and tokens that can simply be dragged and dropped into the VTT. 

But these are no different then those released with LMoP, right?

They are unlocked across all of your games. Whereas the ones in LmoP are only available in games created with the module. For your purposes, the LmoP module contains everything you need to run the adventure. 

The MM compendium entries are not journal entries (like in LMoP) until after you drag them to the map.

Thank you.