Size of framebuffer lookup table
Assuming that by framebuffer they really mean palette table, then the table consists of 256 entries, each encoding an RGB color ("true color"). An RGB color takes 24 bits (3 bytes), 8 bits per color component, so in total we need 256$\times$3=768 bytes. That said, it may be easier to access the table if each color takes up an entire dword (32 bits, 4 bytes): for example, indexing could be for free in certain processors. In that case the table would take up 256$\times$4=1024 bytes. However, given the data at your disposal, the best guess would be 768 bytes.

Palette tables are most celebrated for their use in the popular GIF format. GIF uses a color palette consisting of 256 colors (in its most popular version), one possibly being reserved for "transparent", and the colors themselves are stored separately, usually as "true color" 24-bit values. The color table indeed uses 3 bytes per color, for a total of 768 bytes.