Hello Gerard and welcome to linux.org
Don't think that I am for one moment being obtuse but your question is like "How long is a piece of string?"
... but valid!
There are over 200 relatively mainstream Linux Distros, 500 with a little more digging, and then perhaps a total of 1,000 counting those in the wild not yet come to our attention.
So you will see straight away the difficulty in recommending one over another.
Do I take it you have Googled eg "linux touchscreen support" and read a bit?
Desktop environments factor in, known as DEs, they can be read about here
https://renewablepcs.wordpress.com/about-linux/kde-gnome-or-xfce/
Of those listed, the one that "they say" is most user-friendly to touchscreen users is GNOME. I do not have any statistics to corroborate that.
Some of what follows may confuse a little, by all means ask for clarification and I or others here will answer.
Display Server (not to be confused with Display
Manager) can have an impact. For the most part, the largest used Display Server is the X Server from x.org. Wayland is the newer heir apparent (not too keen on it myself).
Some forward thinking Devs (developers) are now releasing their Linux Distro with the option to choose one or the other at login. My main area of use is with X.
Some of the levels of support may vary, including whether they work in your Browser (usually Firefox, but may be Chromium, Chrome, Opera or other).
Factors like two, three and four-finger gestures support may vary.
Sounds like a nightmare? If it helps, I can tell you from my own experience:
- I run, typically about 70 Linux spread over 3 computers, two of which have touchscreens
- They are the Acer Aspire ZZ5761 All-in-One I am typing from, which should fall over in a few minutes and be non-functional for 3 to 4 days. It has nearly 40 Linux on it. And then there is the Toshiba Satellite S70t-A laptop I will retire to while the Acer sulks. Both bad purchases, around 2014 - 2015.
- I can list my Linux for you if you like, and I can tell you that each and every one has some level of functionality with touchscreen.
- HOWEVER, I have both touchscreens disabled from startup, because both of them can cause my mouses to go run a jitterbug with the cursor, right from login. Hope you do better with the Lenovo.
BTW the jitterbug phenomenon with the laptop existed with Windows 8.1 which it shipped with, before I blew away Windows for my totally Linux environment. It was refurbished but did not say so in the advertising.
My best advice is this - arm yourself with a few USB sticks and run what is known as Live Linux to "try before you buy" so to speak.
Check out distrowatch.com or ask for my list, try a few. The live medium will load the touchscreen drivers, it does with all of mine. So you can see what works and what does not, or is not fully functional.
Hope this helps rather than hinders?
Cheers
Wizard