Rear tires are worn down already. Mast will contact lights and overhead doors if new recommended tires are used. Wider tires are only being requested because the truck gets stuck when going from building to building in gravel. This is a small one lift customer that will not buy a second lift. Just feeling for options.

Based on knowing nothing more than what you have provided i offer the following comments & things you might possibly check out and some you need to check out.
1. a 19 x 8 x 15 seems to be a very uncommon tire size. While the tire might be available finding a wheel might be a larger problem as most wheels front and rear are specific to the OEM manufactuer. Uniqueness is generally found in the center plate off set from center position (either to the right or left of horizontal center and plate thickness, bolt hole pattern & hole design (i.e. amount of lead in taper for centering the wheel on the stud)
2. since you (via your customer) are wanting to lower the overall height by 1" at the drive tire end what are the plans for the rear tires, otherwise you have a unique verson of a California rake - this is not good when it comes to maintaining lift truck stability - the trucks center of gravity would move forward & slightly downward.
3. Obviously, for P L reasons you would need to get the manufactuers or their authorized representative approval for such a modification.
4. Is the mast lowered height the issue or the OHG?, if OHG is the issue then lowereing the OHG might be easier.
5. Tire sizes are selected by the truck manufacturer by Tirm & Rim load rating rating charts 9the ymaybe called something else today) that specifiy the max imum weight the front or drive tires cam be sujected to with a full basic load capacity rating usually with a standard (universal) compound tire for the front drive tirs or full empty for steer tires.. I have seen smaller (narrower) tires used when a polyurethane tire is specified and stated on the nameplate). Polyurethane tires generally have a capacity rating of 200% of that of a standard or (universal compound tire).
6. And going to a wider tire/wheel may present issues with interferernce with brake lnes, axle housing etc. on the inside.

GL