A LIT combines the trigger logic of market-if-touched with the price control of a limit-order. Nothing is visible in the order-book until the trigger prints; then the limit goes to work and may or may not fill.
The trade-off is the usual one: you will never pay more than your limit, and you may end up with no position at all if price trades through the trigger without pausing.
Example: trigger 78.00, limit 78.02 on a buy. Price ticks 78.00, the limit is submitted, and because the market is offered at 78.01 you fill instantly. If instead price collapses from 78.00 to 77.80 in one print, the limit rests unfilled at 78.02 while the market runs away below you.
Related: market-if-touched, marketable-limit-order