It will cost about $60 plus tip from Ballys. The taxi cab authority has a chart that lists prices from the airport so you have to add the mileage from Ballys to the Airport and from the airport to Lake Las Vegas.

From Bally to Lake Las Vegas/Reflection Bay cost about $50.30 one way

Sixteen taxicab companies service the Las Vegas valley. When you enter a taxicab, the driver will start the taximeter (referred to as the “drop”) and an initial charge of $3.30 will register. If a taxi ride originates at McCarran International Airport, an additional airport surcharge of $1.80 per trip is added to the taximeter. After the initial “drop”, the taximeter will assess a fare of $2.40 per mile ($.20 for each 1/12th of a mile traveled). If the taximeter senses that the taxicab is moving less than 8-12 MPH, the taximeter will assess a charge of $.20 (twenty cents) every 24 seconds ($30.00 per hour waiting time). That is why the taximeter continues to accumulate charges even when the taxicab is not moving. Once the taximeter senses that the taxicab is moving at a speed greater than 8-12 MPH the fare calculates on the actual distance traveled.

lake las vegas easy 50 bucks.
why not considering renting a car it is cheaper by the day even with gas.