As you can see in the image of the time train below, there are three letters: "ELB". Now, it stands to reason that these are probably Doc Brown's initials i.e. Emmett Brown. This indicates, though, that Doc has a middle name starting with 'L'. What is Doc's middle name?
The Back to the Future Wiki page on Doc cites the episode Put on Your Thinking Caps, Kids! It's Time for Mr. Wisdom! as saying the following:
In the episode, Mr. Wisdom refers to "Emmett Lathrop Brown". Marty replies "Lathrop? So that's what the "L" stands for!"