Lo Alecha Hamelacha Ligmor is by myself (Jeff Klepper) and Dan Freelander, performing together as "Kol B'seder" since 1974. Sheyibaneh is by Motti Giladi and was added by some camp Ramah kids many many years ago. We also wrote the popular versions of Shalom Rav, Modeh Ani, and a bunch of other Hebrew and English songs...Kol B'seder's versions of Shalom Rav and Modeh Ani are not known in the "frum" world, but are actually quite popular and are both included in the NFTY Fifty songbook. There are several Conservative/Reform artists who have had one song cross over to the "frum" community, but who are not well known within that community. It doesn't help that they aren't acknowledged when their songs are used. In addition to Lo Alecha, another example would be Debbie Friedman's "Alef Bet" song.
Jeff's post explains why the "Sheyibane" part of Lo Alecha is missing from their songbook. The Kol B'seder songbook is a great resource, especially if you teach elementary school and/or Reform, Conservative, or unaffiliated kids. Two songs I'd recommend are "Ten Commandments" and Etz Chayim" which are both a lot of fun.
Amazon has their songbook here: