Many people use a combination of Casper and Munki. I haven't spun up a Munki server but it's on my to-do list this summer. Think of Munki as "software update" but for non-Apple softwares.
LANDesk is not a great Mac management product, and I'm being kind there, I used an older version a few years back at another job (vers 8 and then vers 9) and it was always painful on the Mac side. Its fine for Windows though.
While it can do what you're saying about reporting on 3rd party application updates, don't be fooled into thinking its anything immediate. As I understood it, the way it worked was the LANDesk team needed to get the updates first, pull info about them and then update a list that would get pulled down to your server. So, if there is a zero day Flashplayer update, it could be a day or two before it shows up. You'd likely know about it from reading this forum before seeing it on your LANDesk server.
Outside of that, most other stuff never worked too well on the Mac. It can't hold a candle to Casper Suite. I hope for your sake and sanity that your org doesn't decide to go with that. You'll find yourself wrestling with the product to get it to do what you want more than anything else.
I also acknowledge that my information about it is a bit out of date, so its possible it works a ton better today. But I'd be hard pressed to believe they've come close to matching the capability of the Casper Suite.
There's no reason why you couldn't build this logic into JSS with Extension Attributes + Smart Groups to scope out computers that need a certain version of software and to be able to either push or alert users about the update to install via Self Service.
worth voting up a somewhat related feature request if you haven't already
Patch Management Integration
https://jamfnation.jamfsoftware.com/featureRequest.html?id=662