Hello BurtJordaan,
First, I'd like to say this is very well done. Keep in mind, I'm only self educated, not an expert.
Now, I will offer a few ideas that may spark some insight for a more complete concept of what's involved.
1) I presume this Lattice is the fabric of Space-Time.
Issues: If this lattice is expanding then only a few possibilities present themselves:
A. More lattice rungs are being added at the edge of the Universe.
B. More lattice rungs are added periodically throughout the lattice.
C. The lattice rungs themselves are stretching without new rungs being added.
I dismiss (A) because that would increase the size of the Universe but the distance between the Galaxies would remain constant.
I dismiss (B) because that would screw up the symmetry, like playing chess on a board where on occasion each board square (lattice) decides to abruptly quarter itself.
That leaves (C) which I believe is your point anyway.
2) In order for Galaxies to be spreading apart this fabric must be having some effect on the matter involved. So the tricky part is showing how this lattice can get bigger without making the distance between particles also larger. If the distance between particles were growing then matter itself would have to grow along with the expansion giving a net gain of zero effect.
In other words, if you doubled the size of everything in the Universe, you wouldn't be able to detect any change, as all measuring rulers would also double in size.
So one must make a decision: This lattice has no effect on matter or it does. If it does, then at what Scale does it fail in growing the distance between particles. If it has no effect on matter, then the mean distance between Galaxies isn't really changing.
The solution is that the lattice does control the distance between particles. But in order to avoid a net gain of zero, we must accept that the lattice doesn't have a rigid universal symmetry. That in some places the rungs of the lattice are shorter than in other places.
So how can this be? Well, the lattice is actually 4 dimensional. But I know that's hard to show in an image. It has 4 axis directions of X,Y,Z,T.
Now the concept behind Relativity is that the size of a lattice 4D cube is always a constant volume. As Matter gets involved, the T axis stretches (time slows down) and the remaining 3 axis shrink, thus keeping a constant volume. This is the logic of why an object changes shape as it approaches the speed of light.
As Matter accumulates in an area, the lattice shrinks on X,Y,Z axis and stretches on the T axis. How do we know this is true? We know by experiment that The lattice can be flat, or curved, and twisted. Because Relativity predicts Gravity Waves can propagate by altering this lattice fabric, then we must also add expansion and compression to it's list of tricks.
So, if the early Universe was very flat and symmetrical then after particles began to appear, condensation took place due to electrical effects. As condensation reached a point where the lattice starts changing it's shape and shrinks around the particles allowing Gravity to become manifest.
So what is Gravity?
Here is an cross section (XY) of your lattice with a concentration of matter in the center:

- Typical sample of Gravity affected lattice
Click image to enlarge.
Now imagine that the T axis is at 90' from this lattice (towards you). Next realize that matter/energy must always be in motion or it ceases to exist. It is basically coming towards you (the 90' thing) at the speed of light. During this travel it goes through many shifts in symmetry. At some point it completes a T axis shift and is now in a new location. I hate using the word Random, but let's assume the new position is a Random function. How far can it travel on the XY axis in the time allotted? I have drawn a circle to show the hypothetical maximum range it can travel on XY before it's new location is defined. It's like a cone with the point of origin being the sharp end of the cone and the circle drawn is the large end of the cone showing all the probable points it can reach in the T axis interval.
Notice anything unusual? Yes, there are far more places for it to relocate to in the direction of the greater lattice density. So Matter tends to migrate/gravitate towards anyplace the lattice is denser. So the variable density lattice explains Gravity.
Also note that if no new rungs are ever added to your lattice, that the increase in lattice density due to matter migration must come at a price of stretching the rungs length where the matter isn't. Namely between stars and especially between Galaxies.
This sounds like the effect of Dark Matter (denser lattice) and Dark Energy (lattice stretching). But this also means that if you could build a ladder spanning the distance between two remote Galaxies, and given that they have no relative velocity difference between them, that while it may appear the Galaxies are growing apart, the ladder is stretching along with them and not growing new rungs. So from this can we actually say that the Universe is stretching or expanding? Or are we simply seeing the effect of lattice condensation inside Galaxies at the expense of lattice stretching between Galaxies?
Since Dark Matter (dense lattice) creates a Gravitational Lens, then what kind of lens is being created by Dark Energy (stretched lattice). And given all that, how can we be sure of any form of distance measurement through all these deformations in our Universe? If our Galaxy is denser (smaller) than it was many billions of years ago and the light that left a distant but equal sized Galaxy has traveled all this way while we have all been shrinking during that time span, would the light appear red-shifted (longer wavelength), based on how far back in time it left it's home Galaxy?
Of course this is idle speculation, but I've heard others offer alternate explanations on why light red-shifts over great distances and time, without supporting the concept that the Universe is growing larger by the moment. Is the Hubble constant a measure of Universe expansion or local shrinkage? Fun thought that is.
One last thing.. as I have to head home now.. I'd lose the "Infinite" part of your lattice concept. Infinity can not exist by it's own definition. As a concept.. fine.. but in the real world.. it's no more than an unachievable goal.
Best wishes,
Dave :^)