Minimum and Recommended specs were released for the Linux port of Tomb Raider, they are as follows:
Minimum
OS Ubuntu 14.04 or SteamOS 2.0 (64-bit)
Processor Intel i3 or AMD FX-6300
RAM 4GB
Graphics card 1GB
NVIDIA GeForce 640 (driver version 364.12) or 2GB AMD 5770 (driver version MESA 11.2)
Recommended
OS Ubuntu 14.04 or SteamOS 2.0 (64-bit)
Processor Intel i5
RAM 8GB
Graphics card 3GB
NVIDIA GeForce 760 (Driver version 364.12)
Of course just about any flavor of Linux will do, obviously. 😛