In the second third of the trip, Lydia is going to use 60 liters of fuel / 3 = <<60/3=20>>20 liters of fuel.
In the final third of the trip, she needs half of this amount so she is going to be using 20 liters / 2 = <<20/2=10>>10 liters of fuel.
So in the first third, Lydia used the remaining amount of fuel which is 60 total liters of fuel – 20 liters of fuel in the second third – 10 liters of fuel in the final third = <<60-20-10=30>>30 liters of fuel.
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