Here is a part breakdown of your appliance:
Model LTE5243BW0
If you were able to stop the water by turning the timer off it usually means the water valve is ok. If you had to turn the water valves on the faucet off to stop the water then it could be a bad water valve.
Click for water valve:
Part Details - WHIRLPOOL Inlet water valve, part number: AP3094541
I would start with checking the pressure tube that goes from the side of the tub up to the water level switch. Check for the ends falling off, small holes or it being pinched. Check for anything that would affect the pressure between the tub and the water level switch.
Click for pressure tube:
Part Details - WHIRLPOOL Hose, part number: AP3598454
If that looks ok then check the water level switch, you can test it with a meter for continuity, it is in the console.
Click for water level switch:
Part Details - WHIRLPOOL Switch, water level, part number: AP2947148
Click for testing instructions:
Testing and Replacing Water Level Switch for Whirlpool Washing Machines - RepairAve.com