You have the option at the start of a game to create a log file which records every die roll, all the text you have written to each other whilst playing and everything done to the mapboard and counters.
You can then copy and send the log file to your opponent. On receipt you open it in Vassal just as you would do a saved game and you can click through it line by line. You will see all die rolls and all text and everything that is done to the mapboard and game counters. It is possible to 'Undo' dierolls and moves, but the logfile records the 'Undo'.
The biggest difficulty I forsee in playing by email is not the security of the logfile; it is handling impulse based turns and opportunity fires. Even allowing each other to roll for your defence, you will still have the problem of ascertaining hex by hex if there is going to be an opportunity fire. Then you have the continual passing of impulses from one player to the other, which can be very rapid at times. The difficulties of play by e-mail are not insurmountable if you are determined enough, but very labourious.
If you can get your opponent on Vassal with you, then you can play normally. And if you use voice over broadband, you dont even have to type as you can talk to each other. (We're using Skype very successfully - and its free)!
Stick a picture of your opponent on top of the monitor and its almost face to face.
Yeah, that op-fire thing could really kill the enjoyablility of LnL PBEM. It's hard for me to do anything requiring real time though, as I tend get my gaming in small, unpredictable chunks rather than large scheduled ones... And it's really difficult to find any wargamers in the area I live; too much Dungeons and Dragons and not enough tanks!!!