Missions are delayed when you shoot down their craft, however this can also trigger retaliation missions, although those, too, can be delayed. As I currently understand it, missions are often run over weeks or even months, frequently having multiple days between one wave and the next. When you shoot down a craft (or probably also if you assault the craft on the ground and take it out), you add as much as a week to the mission before the next wave can appear. You should be able to delay lobstermen's prominence in the game by shooting down their craft, but that will also put you at risk of getting a base assault by lobstermen. If you research a navigator and build a transmission resolver as fast as possible, you can get better control, allowing you to actively choose how you wish to deal with lobstermen rather than leaving it up to chance. Also, having a transmission resolver gives your base a potentially strong defense: you will spot retaliation scouts very quickly, you'll know they are on a retaliation mission, and you can shoot them down as soon as they show up. If you stay on top of the scouts, you drastically reduce your chances of being detected. You can get the best chances of avoiding lobstermen by shooting down terror mission and retaliation mission scouts, and letting as much as possible on other missions get through. Also, if you shoot down all infiltration ships that aren't lobstermen but ignore those that are, you're still reducing infiltration rates while avoiding starting lobsterman retaliation missions.
So in the end, if you need to stay away from lobstermen, I'd recommend getting the Transmission Resolver as early in the game as possible. But also, it can be helpful to learn how to kill them. I'm no expert on it but I know they can be stunned with thermal tazers and you can blow up the stunned lobsterman with a grenade, also there's probably a way to unlock vibroblades sooner if you know how to go for them.
