As usual, I second Nishikata with one caveat. Apply to one other safety school other, than your home uni (awesome that you have an Ivy home uni— cherish this). There are schools in the top 50 (based on your info, I'd recommend #20-#50 depending on how much courage you have —— or apply to two other safeties, one around #20 and around around #40) that have BRILLIANT professors in lattice QFT.
Start the Excel sheet man.
Step #1: Start at MIT, and work your way down hahah — https://www.usnews.com/best-graduate-sc ... s-rankings
Step #2: The Uni's research page for the topic you're interested in — http://web.mit.edu/physics/research/npt/areas.html
Step #3: You got lucky with HEP. Use InspireHEP (alternatively arXiv, Google Scholar, Research Gate) to see if they are activing persuing research you think is cool. Keep an eye on the publications in recent years. Linearly decreasing (if you see exponentially decreased, move on, they are retiring/leaving) may be a bad — http://inspirehep.net/
#2: Name from HEP-th page, Iain W. Stewart
#3: Absolutely stellar profile, http://inspirehep.net/author/profile/I.W.Stewart.1