Currently running Mate 19.04 - originally shipped with Mate 16.04 LTS (from los-alamos linux). It comes with two batteries. The Sanyo 01AV405 battery goes from 50% power to 4% in one cycle -- which seems wrong.
Here are some screenshots
How old is the battery? Often when they get to be a couple of years old or more, it's simply just getting to old to properly hold a charge. Lithium ion batteries have a very finite life span, usually ~3 years or so from manufacture.
Hello janpolak
open a terminal and enter the following:
upower -i `upower -e | grep 'BAT'`
note that you can print this to a file if you want to, thus
upower -i `upower -e | grep 'BAT'` > filename.txt
Look at the values for "energy-full" and "energy-full design". Does that give you any further information?
Reference:
[https://vitux.com/view-detailed-laptop-battery-report-on-ubuntu/]
If you bought your Thinkpad reconditioned after it was used in a company, it may have spent most of its previous "life" sat on a docking-station. The battery may not have been "cycled" enough - this can seriously shorten the life of lithium batteries.
A word of caution - if you decide to replace the battery, buy a Lenovo original replacement. Some lithium batteries now have technologies included to prevent generic batteries from working/working well.
Hope that helps. 
The computer was bought new, from Los Alamos Linux in 2016. It has two batteries
- BAT 0 is working great -- vendor=SMP, model:=00HW023, serial=1035, energy-full-design=23.5, energy-full=21.4, capacity=90%, technology=lithium-polymer
- BAT1 is the problem -- vendor=SANYO, model=01av405, serial=2477, energy-full-design=26.33, energy-full=22.07, capacity=83%, technology=lithium-ion
The issue isn't short battery life (although it is short) - it's that one minute it says 50% remaining, the next it says 4% remaining.
This machine came with two batteries. BAT0 is the battery that is drained to 4% before BAT1 kicks in. Yet, BAT0 is working fine, and BAT1 is having the issue described.
I just completed a tlp recalibrate BAT1 -- which also resulted in the battery going from 50 to nearly zero in one second as reported here by many users
I'm going to keeping the battery charged to 100% for a few days since, like other users, I use tlp and report back.
Edit
Worked brilliantly. Set TLP to 99 start charge and 100 end charge. I kept it charged for a couple of days and re-ran tlp recalibrate BAT1 and I got another hour of battery back