1.I would do the math to get the square inch volumn of the lines.
2.Measure the volumn in square inches of the container the fluid is in and do the math to determine the square inches it takes to hold the amount of fluid thats in the container. (measure only the occupied area of the container)
For intance you may have a container that is 12 square inches with 12 ounces of fluid in it. Which equates to 1 ounce per square inch.
3.With the results of those two calculations you can quickly determine the amonunt of liquid it will take to fill the lines.
I am sure someone else has a better way but I think this will get the result.