Interleave lower bound is like a rule that tells us how fast we can put two lists of things together. Imagine you have two sets of toy blocks and you want to combine them into one big set, but you have to put them together a certain way.
Interleave lower bound says that it takes at least as much time to combine two sets of blocks in a certain way as it does to write down the blocks one by one. So, if you have 10 blocks in one set and 10 blocks in the other, it would take at least 20 steps to combine them according to this rule.
This means that if you have a computer program that needs to combine two sets of things, it can't go any faster than this rule allows. So, if the sets are really big, the program might take a long time to complete.
It's like having to follow a certain recipe when cooking. You can't just throw everything together in the pot and expect it to come out right. You have to follow the instructions step-by-step to get the best results.