Armageddon style games are basically their own variant, and are actually played fairly often in high profile events as tie-breaks. They could be added to lichess fairly easily, since the only thing that changes is the initial times and that a black draw is a win.
An example seek would go like this,
base time control: 5 minutes
Wager for black pieces: 3 minutes 2 seconds
Would match you up with another person seeking a 5 minute game. your wager would be compared to their wager, and the lowest wager gets to play as black, but must play with the amount of time that they wagered. White gets the base time control. When accepting a seek (by clicking on the graph) you would first have to input a wager. and of course at no time during this process are the wagers visible to potential opponents until the moment they are compared.
An example seek would go like this,
base time control: 5 minutes
Wager for black pieces: 3 minutes 2 seconds
Would match you up with another person seeking a 5 minute game. your wager would be compared to their wager, and the lowest wager gets to play as black, but must play with the amount of time that they wagered. White gets the base time control. When accepting a seek (by clicking on the graph) you would first have to input a wager. and of course at no time during this process are the wagers visible to potential opponents until the moment they are compared.