The LCIII has 512KB of VRAM standard, soldered onto the motherboard, which cannot be removed, which gives you either:

Up to 16 bit (Thousands) of colours on a 12" monitor at 512x384

Up to 8 bit (256) colour on a 13 or 14" monitor at 640x480

and according to Apple, up to 4 bit (16 colours) on a 16/17" monitor at 832x624 (I've never run my LCIII at any res greater than 640x480, but I recall Apple saying that without a VRAM upgrade, the LCIII only supported 16 colours on those displays, despite 512KB normally being enough to run a display at that resolution at 256 colours on other systems)

You can put a 256 KB VRAM SIMM into that VRAM slot, expanding the total amount of VRAM to 768KB, which will give you:

Up to 24 bit (Millions) colour on a 12" monitor at 512x384

Up to 16 bit (Thousands) colour on a 13 or 14" monitor at 640x480

Up to 8 bit (256 colours) on a 16/17" monitor at 832x624

The LCIII takes the same kind of Apple VRAM SIMM as other 68k Macs, they're fairly easy to find if you know where to look, and the 256KB ones are fairly ubiquitous, since they were OEM in LCs, LCIIs and LC475s. If you want to upgrade the RAM, you'll need a 72 pin SIMM, preferably either 16 or 32MB.