A "lattice" is a framework that contains open-gapped criss-crossed strips.

Criss-crossed strips are multiples of the letter "X"

The letter X, in Hebrew, is called "tau."

"Tau" in Latin script is "T"

The Badge of Royal Arch Masons is called the "Triple Tau."

You can see it displayed on the right side of the page here:
[link to en.wikipedia.org]

Notice how the three "T" (tau) shapes form a kind of lattice?

And remember that "tau" is written as "X" in Hebrew?

So it's a double pun, which serves to confirm the interpretation. BOTH forms of "tau" form lattices.

But the Triple Tau lattice is formed ONLY by the Royal Arch badge.

Meaning? The Nobody is kept suppressed BY the Royal Arch Masons.

That, in fact, is their ultimate purpose, for which they've prepared literally for generations.

So he "peers through" their "lattice" (i.e. their efforts to suppress him).

Notice, however, that he doesn't try to "break through."

And why?

Because he doesn't have to.