Choosing the correct LVL beam size
Nope, a 2 ply 1-3/4" x 11-7/8" LVL can't span that long with this much roof on it. With a 19' span (and completely guessing on the roof span and live loading for your area) you're looking at at least a 2 ply 24" LVL or a steel beam that would be impossible to install at this point.

The best solution to open this up is to run a 3 ply 11-7/8" LVL full length but with an intermediate support in the middle making two 9.5' spans with 1 beam. The intermediate bearing post will have 18,000+ pounds on it, so you'll need a PSL or steel column.

You'll also need a new column the same size directly below it in the basement. Your existing strip footing won't be able to handle a point load that large, so you'll probably need to pour a new pad with a bunch of rebar there, and that size changes based on your soil type and conditions. 

So like the other answer said, get a contractor or an engineer to help you. I'm making educated guesses on everything based on one photo and knowing you want a 19' clear span, so take that for what it's worth.