Hm, that's an good question. I know you can't stop others from drawing on the map, but no idea if you can prevent players from editing their own initiative. Suspect you can't. Either way, this is an more of an inter-personnel problem, and should preferably be dealt with in that way. Even if there is a technical fix for this, you're just mitigating the actual problem of the player cheating, and they can attempt to do so in other ways as well, such as editing their stats temporally so they have high modifiers in their rolls, and then change things back. If you want to keep the player, but don't trust them for their own initiative, you can set up a copy of their sheet(that only you can see/edit) and declare that you roll the players initiative for them. This still doesn't fix the core problem, and they would likely try to cheat in some other way.
