The Infinite Horizon
Though we have words for it, the human mind cannot comprehend infinity. Easy enough to say, "it goes on forever," but the very nature of the concept will always remain beyond our grasp, for such is the definition of infinity: that it goes on, and on, and on ...
Is the Lattice actually infinite? We must be satisfied with the answer that if it is finite, we might some day prove so. But there is no way of proving that an edge or border or terminus does not exist -- one cannot prove a negative.
Suffice it to say that neither man nor alien has found any limit to the Lattice, and is quite unlikely to do so for many millennia to come.
Infinite Mass
If the Lattice is indeed infinite (and we must disregard any theories of a curved, closed Universe, if we are to assume so), then cosmologists must grapple with the irreconcilable datum of an infinite amount of mass existing in a two-dimensional plane, towards which all other matter in the Universe would be drawn. In a steady-state Universe, matter drawn into the plane of the Lattice would be re-created elsewhere. In a Universe born from a primal singularity, though (of which the openness or closedness is to be determined), an infinite Lattice would doom the Universe to eventual collapse. However, under either theory, only an infinite Lattice would not collapse upon itself, given enough time; so, the age of the Lattice becomes a critical factor in determining its extent -- perhaps the spacing of the Lattice worlds was initially more than its current 5.1 light years, and indeed the Lattice is contracting under its own weight. Not enough data exists to estimate the age or potential collapse of the Lattice. Neither the Big Bang nor the Steady State theory can currently reconcile an infinite Lattice ... but no observation as yet has hinted at any limit to it.