Having a LAN option doesn’t mean you can’t have online multiplayer, the reason many games don’t have LAN is that most multiplayer games these days have player progression and if you’re offline then they can’t manage that and you could cheat. If that’s not something that could be an issue (you have no player progression) then LAN can be something you can consider, and for tournaments that’s definitely appreciated since they can avoid connection issues.
However, that wouldn’t prevent cheating. The way many cheating programs work is by accessing variables that are calculated on the users machine. That’s why Diablo 3 was online only, they took some of the components like enemy AI and damage calculations and put them on the server so that people couldn’t try and cheat those, which was important to avoid cheating when they had the real money auction house. On a LAN you have to have someone as the host, so there isn’t a place you can calculate variables without a user technically having access to it and being able to cheat. Though one would assume that if it’s LAN then you would pretty easily be able to check if the other player is cheating since they should be nearby.
Still, you’re limiting the people you can reach if you’re targetting tournament type stuff, people have to like your game first to consider it at that level and they aren’t going to play it if it’s LAN only.
That’s such a minor difference compared to other FPS games. You need a unique feature that’s easy to understand and gets people excited to play your game. For example, Battlefield is known for high graphical quality and big maps with vehicles.