I don't trust the Java website's check Java is installed properly, I've also had same message it couldn't find it but LW worked fine. I'm guessing that check is not set up for Java 6.
As for using Java 7, you will need to use LimeStart in order to use LW with Java 7. That's a workaround for LW having problems opening directly with Java 7.
LimeStart for Windows via MediaFire. ie: use LimeStart for opening LW instead of opening LW directly. The LimeStart installer will replace the shortcuts with same LW name but link to the LimeStart program instead.
And finally,
LPE Connection Fix installer, also via MediaFire.
The crap you refer to packaged with the LW installers included LimeStart, connection file, optional settings for safe use & an optional blocklist. Perhaps if you had installed that crap in the first place you wouldn't have had all the problems you are having. lol
It seems everyone who downloads LPE or a version of LW 5 from other sources & is using Java 7 ends up coming here & finding links to the LimeStart-Java fix installer (about 60-70 downloads/week, though was over 100/w mid last year.)