Lochmere Serpent's ability
Yes, you can do this.
All islands have the (unwritten) ability of Tap: Add {U} to your mana pool. You can activate this ability any time you have priority. You simply tap the land to get {U} in your mana pool, which will remain there throughout the current step/phase. You can then spend that {U} and sacrifice your now-tapped Island to pay your Serpent's ability cost.