Here are some past discussions on 'longevity' versus 'hardness':
https://www.soapmakingforum.com/thr...t-soap-bar-from-dissolving-too-quickly.74557/See posts #8 and #11 in particular.
https://www.soapmakingforum.com/threads/help-needed-hardness-and-longevity.77011/Excellent source for your questions regarding the difference between the two & how to achieve longer lasting soap, but still foster the other qualities you want in a bar.
Regarding the question of SL contributing to longevity, it was something I read on a blog reporting testing done with soaps using the same recipe with and without SL, and how long the soaps lasted. As I recall, it was anecdotal, not scientific, but the accompanying pictures seemed to support the anecdotal reports. It's been quite a while since I first read it, and don't recall exactly where I read it, but I have seen it a few times & if I run across it, I will add a link.
Edit: Okay, here's a link where SoapQueen says it lasts longer in the shower with sodium lactate. Not sure if I'll find another link to attach, but at least here is one:
How to Make Soap Last Longer in the Shower - Soap Queen
Another edit: Here is a discussion with anecdotal reporting:
Sodium Lactate vs Salt & Sugar