Once, there was a mighty space empire, suffering from a famine after their enemies introduced a genetically engineered crop blight. They tried to save themselves by creating a blight-resistant strain of genetically engineered tomatoes. But the tomatoes became sentient and turned against their creators, carving themselves out a slice of the galaxy.
Among other techniques, they can grow infiltration agents that resemble other species, as well as non-sentient tomato drones that can be controlled remotely.
Shortly before the Spoon of Destiny Saga, the LNH fought off a Lycopersicon invasion. It's theorized that they chose this time to invade because they grow well in high temperatures and carbon-heavy atmospheres, and may have been pushing Earth-20's technological development towards that goal.