The entire kitchen is dedicated to vegetarian cooking - no meat or fish is ever used on the premises. Every dish is vegetarian by default, so cross-contamination from meat or fish is impossible.
Lust is a 100 percent vegan restaurant. Because the kitchen contains no animal products, every dish is automatically vegetarian. No per-dish markings indicate vegetarian status, but the entire menu qualifies.
The official menu marks vegetarian dishes with a Thai symbol, and the restaurant offers many vegetarian options. Staff are reported as knowledgeable about vegan options, which likely extends to vegetarian ones.