I forgot that in the Mint link (had it for Ubuntu), thanks for the hint.

Regarding your screenshots:
That's exactly how far I got but it didn't change anything with my WINE version. Update manager didn't find anything newer on refresh and neither did Synaptic although "WineHQ" has been added and is active.

Use reload button in synaptic, then search for wine packages.
Maybe uninstallation or older and installation of newer version is needed.

That did it. Update manager still doesn't show it but I get Wine 2.11.0 and 2.1 options in Synaptic now.
I'll just throw out my old installation after I finished Tender Loving Care and install the current stable one afterwards, thanks.

First post has been edited accordingly, hopefully it will help Ubuntu and Mint users around here which are no computer scientists.

In update manager use refresh.

Command line:
sudo apt-get update
or for aptitude users (but don't mix it with apt-get, since the tools keep distinct caches)
sudo aptitude update

I already did, but it hasn't changed after the Synaptic update.
Didn't change anything either.
I don't think that "wine 1:1.6.2-ubuntu14", "winehq-devel 2.11.0~xenial", "winehq-stable 2.0.1~xenial", "winehq-staging 2.11.0~xenial", "wine-devel 2.11.0~xenial", "wine-stable 2.0.1~xenial", "wine-staging 2.11.0~xenial" are recognized as the same programs, I'll just add a screenshot.
Nevermind "playonlinux", I'll throw this out as soon as I'm finished with some game in there, same goes for the obsolete ancient wine from Mint.

Yes, so no update is available.
Unistall old and install new version is needed.

i think these long commando chains are bad. Things get confusing very quickly if something in the middle fails.
I would break this down into individual commands
further:
- this has the same typo & -> &&

>> sudo apt install wine-devel winehq-devel winetricks
you only need one of wine-devel or winehq-devel (and winetricks isn't really needed either)
i would even suggest using winehq-stable instead. The normal user probaly isn't interested in installing the development snapshot that gets updated every second week( potentially breaking things) :)

i would just link to the winehq wiki instead of duplicating the installation instructions. the wine people will keep their wiki up-to-date if things change (= less work for you to maintain this post ;) )

>> mv ~/.wine ~/winebck
this will fail if the user hasn't used wine before and ~/.wine doesn't exist. if it fails the commands behind won't be executed. If he has used wine before then he might get annoyed that his installed programs are suddenly gone :p
using the existing ~/.wine will likely work just fine

>> export WINEARCH=win32 && winecfg
Do you really explicitly need a 32bit prefix? With current wine versions just using the default 64bit one should mostly work.
btw this can be shortened to
WINEARCH=win32 winecfg
and since you only need it to create the prefix, you don't really need to run winecfg. this will also do
WINEARCH=win32 wineboot

I've run into a problem with TLC, running on Ubuntu 17.04. After a while, the videos will no longer play by themselves. And you cannot force them to play either. Hitting the "pause" and "play" buttons that appear at the bottom of the screen will do nothing. The only thing you can do is scroll the slider bar from left to right with your mouse, and the video frames will advance to the end and allow you to continue, but you will obviously miss out on the audio and it clearly ruins the experience.

I'm wondering if I need to download/enable any dll files in Winetricks to fix this problem. If anyone has any thoughts that would be awesome. Thanks.

I tried to run the game on Debian 11 with the packaged wine version. The --disable-gpu option did the trick for me. The game now runs without problems. Thanks for sharing.