http://www.fonejoy.com/genuine-lg-w150-urbane-watch-bl-s3-410mah-battery-eac62618501.html
Had the same problem and yes I bought a new cradle too. The link supplies a replacement battery with carriage for about £21. You need Torx 4 bit and follow the tear down. Getting the band off was the worst bit, go very carefully with taking the connectors off but otherwise Ok. Just done mine and is now charging up fine. On arrival the new battery had 30% charge. Recommend the Ifix tool kit for jobs like this!
PS don't worry whether it's an LG Watch R or an Urbane they both use the same battery.