As the title says, why not have a lag for the opportunity to break in one game tournament matches? It can be done fairly easily I would imagine as it already exists in Carom on Funkysnooker and would add an element of skill to ensure that nobody could ever be knocked out of a tournament without playing at least one shot.

Carom has it yes...

One flaw to this as the good players will know how much power in for the lag shot and most likely always get break..

What will be better and if it can be added is "Coin Toss" or "Toss the coin" but the players only control is to pick Heads or Tails then the game picks what is shown

Or the way players start can stay the same

Rather than being a flaw I think that is the point. It brings a tiny element of skill to what otherwise can be a one shot lucky knock-out.

Also don't forget that it's not always good players vs lesser players - it can equally be good players vs good players or lesser players vs lesser players where winning the right to break off could be important.

i think its a good idea
knowing how much power to put in it isnt a flaw its a skill that can be learned