My mother has an old Lenovo laptop (bought I think in 2010) with Ubuntu 16.04 installed. It was 14.04 but I upgraded it the last time I was at her place. Her laptop has become very sluggish recently and it's painful to talk over Skype and I tried Duo web and it's still slow and sound stutters and so on.
I am thinking to update her system to more recent one and probably switch her from Ubuntu to Lubuntu or something lightweight. However, she lives far away and I can now for many reasons to go to her now.
I wonder if there is a good way to upgrade her remotely. One of the problems is that she doesn't have a smartphone so if something goes wrong I won't be able to see it. So I wonder if there is a way to keep connected to her laptop to see what is going on and fix it if something breaks during the upgrade? I currently can connect to her laptop through Teamviewer.
The short answer is no, there wouldn't be a way to install a fresh operating system on the laptop remotely. You could create the installation media remotely, however(through TeamViewer, if you have the remote user plug in a USB stick to target, or insert a blank disc), and then attempt to walk your mother through the initial configuration steps. For Ubuntu, this is simply the keyboard layout, network config, and username / system name IIRC. After that, it's just getting TeamViewer installed again and you can take over from there.
If possible, I might suggest a hardware refresh. A decade is a long time in terms of advancements in personal computing. If the laptop does not have an SSD installed for the primary hard drive, that can provide a huge boost in functionality for a pretty low cost these days. I recently picked up a basic 120GB ssd on Amazon for 21$, and it isn't a very difficult swap on laptops (1 or 2 screws for the plastic door, another holding the disk in place, and the cables/adapter piece that slides on and off). Pursuing this upgrade will require you install fresh, or clone the existing hard drive, however.