So just purchasing the Lost Halls of the Dwarven Kings and assembling for a soon to be D&D Campaign (fantastic set btw), and I noticed I am in need of 4x4 and 4x6 rooms in the basic floor design.

Is there a way of getting these as release or finding someone with the skills and know-how of putting one or some together?

I am probably not the best qualified person to answer this... but here goes.
TLX is based on a 3" and 6" footprint, due to its design. 4"x4" tiles wouldn't really work with the design of TLX. What a lot of folks do (myself included) is to just "scale up" maps a bit, ie, just use a 3x6 tile for a 2x4 corridoor, etc. If this doesn't suit your fancy, you can print the 1.5" grid, which will give you 2x2 square 4x4 square and 2x4 square tiles. Of course, for playing D&D you ideally want a 1" grid. There are some sets that include 1" and 2" walls, (HV Sewers, for example), which you then could use to exactly duplicate a map. Generally, however, it is not critical to the adventure to exactly duplicate the map, and an approximation based on the 3" or 6" footprint of TLX works just fine
Hope that helps....
Others may have comments or suggestions to add to this.
Just my $0.02

Greetings Entiago. The answer to your question is both NO and YES.

No, there are no 4x4 or 4x6 tiles within the TLX system BUT yes, it's entilrey possible to make it happen through one of two methods:

1) Use 1.5" instead of 1". Takes some getting used to but if you can think in terms of a grid instead of "inches" then you're good to go.

OR

2) Use the 1", 1.5" and 2" walls provided with the set to create "floating walls", ie walls whose posts aren't always anchored except at either end of a "chain".