Normally if a beta is available it would be found at Lime Wire » Download LimeWire Beta. Also a link leading to it from the download page & those with Pro would have a link to their pro version beta on their download page, but seems it's not publicly available at moment. It might be more of an alpha than a beta.

I am aware LW 5.0 is not too far away from being released, whilst I say that it still might be a while.

Also .. normally beta versions have 'odd' version numbers, such as 4.13, 4.15, 4.17, etc. so we would presume next beta would be 4.19.x.