The Laserfiche SharePoint Integration 8.2 is compatible with Server 8.2 and up. As long as you are using SharePoint 2010 (as opposed to 2013), you should be able to stay with version 8.2 of the SharePoint Integration while upgrading the rest of your Laserfiche system to 9.1.

If you do decide to upgrade the SharePoint Integration to 9.1 (for SharePoint 2013), we recommend that the rest of your system be on version 9.1 as well. When upgrading from the SharePoint Integration 8.2 to 9.1, you should note that Microsoft doesn't support in place upgrades. Instead, Microsoft instructs you to install SharePoint 2013 on a separate machine and then migrate your databases. So while Laserfiche doesn't require that you reconfigure the SharePoint Integration, your original settings likely won't be present on the new machine hosting SharePoint 2013. As far as the steps you'll need to take for this upgrade for the Laserfiche end of things, take a look at the "Upgrading from Laserfiche SharePoint Integration 8.2" section of this KB article: https://support.laserfiche.com/KB/1013459.