I noticed it in passing. I don't think there's a sign on the Herband Walk end. I've done some trawling on the web, and the pattern seems to be that it's referred to formally as Sluice Lane on the Pevensey side and Sluice Road on the Cooden side as it meets Herbrand Walk. But I can't find anything definitive. The other pattern is that, as you say, locals use "Lane" almost exclusively (I've never heard "Road" spoken).