Well, the answer is yes, and the Lewis structure distributes 3xx7+1=22 electrons.......
[I-I-I]^-, going from left to right, there are 7 electrons associated with the leftmost iodine, 3 lone-pairs, and 1 bonding electrons, hence this centre is neutral; the central iodine has 3 non-bonding lone-pairs, and 2 electrons from the I-I bonds, I.e. associated with EIGHT electrons, hence this centre is a formal anion; the rightmost iodine has the same electronic distribution as the leftmost, and this is a formally neutral centre.
Note that when you are next in the lab, try slurrying iodine in water (in which of course it is insoluble!). If you add a little iodide salt (say KI, if you can find it), the elemental iodine goes up into solution to form I_3^(-), and other polyhalides......
