When is Lot Number important for yarn?
Yarns with the same dye lot number were all dyed at the same time. Because dying is a chemical reaction, many different factors can make items dyed at different times turn out differently, even if the dye "recipe" was identical from one dyeing session to the next. The temperature could be different, there could be slightly more or less pigment in a teaspoon of the dye powder, the water used for the dyes could have more or less chlorine from the water treatment plant, the fiber being dyed could have been scoured with a different type of soap, and any residual elements could interact with the dye.  There is tons of information about this on the interwebs-here is one article from Wikipedia.  

All that is to say that it is almost impossible to get an exact match between yarns dyed in different dyeing sessions. It doesn't really matter what the base fiber is, or whether the dyer is an independent dyer working in their own home or a major yarn manufacturer--there will almost always be a slight variation of color between yarns dyed in different dye lots.

So, if you are going to be making something where you have alot of a single color in a block, you usually want to purchase yarn from the same dye lot, otherwise you will probably see a slight (and sometimes not so slight) color demarcation where you have changed yarn. In this picture, someone had to use yarn from a different dyelot to finish the sleeve:


BTW--if you ever find yourself in a situation where you do have yarns from different dye lots, the best way to minimize the issues with color mismatch are to use the yarns from both dyelots at the same time--knit/crochet two rows with one yarn, and then switch to the other yarn. Carry the unused yarn loosely up the side of the piece until you are ready to use it again.  By limiting the area of one color to a small section, your eyes will make the colors blend together and you are much less likely to notice a distinct color change.