When you first install any version of LW you will probably need to use the ConnectFix installer.
LW 5 does run with Java 7 (the most recent version) but only if it is started using the LimeStart utility. The LW 5 & LPE versions we give links to on the forum have LimeStart packaged with them.

Unless you are a torrent user, if you preferred to use LW4 then perhaps 4.14.10 might suit your taste. Installers can be found here. 4.14.10 was my personal favourite version, though 4.16 was also very good.
For pro versions we cannot officially help you there for such copies.