Heat oven to 400°F. Broil cut bagel faces 1 to 2 minutes; return oven to bake.
Flake drained tuna into a bowl. Fold in artichokes, roasted pepper, mayonnaise, lemon juice, and pepper, keeping chunky but evenly bound.
Divide filling among four bottoms on a sheet. Cover with half the Fontina; bake 8 to 10 minutes until filling reaches 165°F.
Top upper halves with remaining Fontina; add cut-side up to sheet. Broil all halves 1 to 2 minutes until cheese melts on both sets.
Close tops over bottoms; rest 1 minute and halve.