Your answer can only be an approximated assumption (an educated guess), since fuel prices are always fluctuating, and the environment through which you travel 178 miles, and the condition and management of your vehicle are all factors that would need to be taken into consideration for a more accurate answer. Also, the model of your 2012 Lexus would play a major part.
If your car has a 25 gallon fuel capacity, and 24 miles per gallon fuel efficiency, then theoretically you could go 600 miles on one fuel tank. This would cost about $125 dollars. If you wanted to go exactly 178 miles in a vehicle with the above specifications, then you would only need to purchase 7.41667 gallons of gasoline, which would cost approximately $37.
The EPA range estimate for the 2012 Lexus LFA is 212.3 mi. in the city, 308.8 mi. on the highway.
The EPA range estimate for the 2012 Lexus IS-350 is 326.8 mi. in the city, 464.4 mi. on the highway.
The EPA range estimate for the 2012 Lexus IS-F is 270.4 mi. in the city, 388.7 mi. on the highway.
The EPA range estimate for the 2012 Lexus IS-250 is 326.8 mi. in the city, 481.6 mi. on the highway.
The EPA range estimate for the 2012 Lexus RX-450H is 550.4 mi. in the city, 481.6 mi. on the highway.
The EPA range estimate for the 2012 Lexus IS-250-C is 326.8 mi. in the city, 481.6 mi. on the highway.
The EPA range estimate for the 2012 Lexus LS-460 is 355.2 mi. in the city, 532.8 mi. on the highway.
The EPA range estimate for the 2012 Lexus ES-350 is 351.5 mi. in the city, 518.0 mi. on the highway.
The EPA range estimate for the 2012 Lexus GX-460 is 345.0 mi. in the city, 460.0 mi. on the highway.
The EPA range estimate for the 2012 Lexus CT-200H is 511.7 mi. in the city, 476.0 mi. on the highway.
The EPA range estimate for the 2012 Lexus RX-350 is 345.6 mi. in the city, 480.0 mi. on the highway.
The EPA range estimate for the 2012 Lexus IS-350-C is 326.8 mi. in the city, 464.4 mi. on the highway.