Is it a lighthouse?

No but it was built to look like Smeaton's Tower, the 3rd Eddystone Lighthouse. Built to commemorate Sir John Barrow who lived in Ulverston , where the tower is a very prominent landmark . Barrow was a founder member of the Royal Geographical Society. We walked to the top (133m) , my two walking companions and I , from where they instructed me on the surrounding landmarks - (extra) including the Blackpool Tower, although my camera did not pick it up