Hello there. An interesting question. LAMS isn't standard in Moodle as far as I know (I remember seeing it there years and years ago and was told not to use it as it didn't work) but I am always a fan of using standard Moodle modules, like the Lesson module, which don't need you to add anything extra. It will be good to hear from people with experience in LAMS integration to see what they have to say.
Comparisons and advocacy
LAMS vs Moodle Lesson Activity
Seems no one is interested in this topic
However, I am trying to setup LAMS+Moodle and see how its different than moodle native lesson plan. Setup is complete and integration validation works but when I try to add a LAMS activity I get an exception which I have posted to lamscommunity. Let's see how it goes, I will keep you posted on my findings.
btw, you can find lams integration discussion in below thread.