Yes Java SE 6 is Java 1.6. Not sure why they use two ways of referring to them. eg: JRE5 or J2SE 5.0 = Java 1.5, etc.
Personally I am unable to run LW 4.18 or LW 5 on my main OSX operating system. I installed another OSX on a partition I had previously set up for Windows XP
(the installation of XP corrupted a few times so gave up after misplacing the installation disk.) Reformatted that partition, installed OSX with updates & LW 4.18 & then LW 5 have run well. I did do 3 archive re-installations of OSX last year on my main drive so looks like something was wrong with the original installation. I should have chosen "Erase and Install" option but didn't wish to have to reinstall all my applications again. lol
So now I run 4.16 on main OSX, LW 5 on other OSX drive-partition. And LW 5 on Windows XP via Parallels, which IMHO is better & more convenient than having to reboot into XP or using the old Virtual PC. I can share files directly between both Windows & OSX using LW, & drag & drop files between desktops also. (My Windows XP is now the 64-bit version which BootCamp does not allow using. BootCamp only allows XP 32-bit or Vista.)