I have a table as follows:
> testsizes size value replicate lane 361 16 6898 1 L1 362 17 10707 1 L1 363 18 1786 1 L1
Based off my comment about interacting the two:
ggplot(testsizes, aes(x = size, y = value, group = interaction(replicate, lane), colour = lane)) + geom_line()
Which gives: