Ltp price gap and market order price

Why ltp in not updating , if i execute at market price which price it will take 566 or 577.25, 577.20?

ltp is last traded price. If there is no trade yet, then it stays where it is and is stale.
Bid and ask price can change without execution.

If you want to buy immediately, you have to pay what others are asking for. So 581.4 upto 150 qty and higher prices for more qty
Same thing for selling, at this moment you can sell 75 qty at 577.25 and will get lower prices for more qty.

No one will offer for 566, price is already up. And so you can also sell for more.
Just imagine this as a vegetables market with multiple buyers and sellers offering best prices that they can offer right now. What the last guy paid/got is just history. Maybe something changed after that and prices updated.

thanks