Are they false ?

[ian_r_h]

I assumed the lwp, java and pulse-shm reports from rkhunter are false positives (I don't use chkrootkit) given that these have occurred immediately after fresh installs of LL followed by rkhunter (and --update) and before Menu/Favourites/Install Updates on 3 different boxes every time; unless my copy of LL 3.6 64bit .iso downloaded from linuxlite.com and rkhunter downloaded via apt-get from the default repo (and different mirrors) were infected to begin with.

These persist even after sudo rkhunter --propupd

Googling found no evidence that these were anything to worry about.

I can't speak as to the rest.