Congrats on the first brew!
Also, congrats on jumping right into being a true homebrewer by deciding to go ahead and fiddle with your first batch by adding lime zest to part of it. Definitely a good idea to wait until you bottle the first 4 gallons, before seperating out the 1 gallon for the lime zest addition.
I like the idea of adding lime, but I wouldn't have thought to do it with a red ale. I might do this with a vienna lager whenever I am able to actually do lagering.