Perfect Lockjaw Deck

On the first and second turns, you should save Quicksilver and Domino - if you have Sunspot, play him. When you draw Lockjaw, snap, then play him at the first opportunity. Once you have Lockjaw down, play Domino, Sunspot and Quicksilver there (in that order if the same turn), to get two-to-three high-cost cards there.

Alternatively, if you don't draw Lockjaw in time, you can play Jubilee to a similar effect on turn 4. Snap if you get a good card and/or you played Sunspot earlier. If you don't draw either by turn 4 and your opponent is in a good position, it is a good move to retreat. Remember that your draw deck is functionally 9 cards large thanks to America Chavez, Quicksilver and Domino, giving you over a 6 in 9 chance of getting Sunspot, Jubilee or, of course, Lockjaw on your first turn.

Use the 5th and 6th turns to win a different location, thanks to your 5 and 6 cost cards in you've drawn throughout.

Note: if you don't have the cards, you can swap out the 5 and 6 cost cards for your best ones (irregardless of cost or play conditions)

Edit: changed the optimal 6/5 cost cards thanks to suggestions and personal edits