What will LogMeIn Central be using to patch third party applications now that Kaspersky Software Updater is no longer supported by Kaspersky?
First of all sorry for the late response.
Kaspersky indeed stopped the support of KSU as a generally available product (and merged it into their other offerings), but as we OEM the product, the KSU included in LogMeIn is supported.
Yes, LMI uses the Kaspersky Software Updater to patch third party applications such as the Flash plugin, Acrobat Reader, etc. So if you enable third party patching through LogMeIn Central, LMI Central deploys/installs the Kaspersky Software Updater on the managed PCs.