That is not really correct. As Dima said, if you are starting out, using Python 3.7 is recommended.
What is not correct is your starting premise of "I installed Python 3.4 on Windows XP. Works fine.".
Windows XP reached its end of life 5 years ago. In fact, Windows 7 will reach its end of line in Jan, 2020.
Coincidentally, Python 2.7 will also reach its end of life in Jan, 2020. Python 3.4 reached its end of life over a year ago. I am not sure when Python 3.5 will beretired, but I would expect that to happen within a year.
So, "Python 3.4 on Windows XP" does not "run fine". It is running without any support or security updates.
Lmfit is an all volunteer effort. We really only support one version at a time, have no updates for older series other than to say "get the latest version". We try to support versions of numppy and scipy that were released within the past two years, but don't actually guarantee that. The next version (0.9.15) will be released before the end of the year and will be the last version to suppot Python 2.7. At the same time, we will release lmfit 1.0 which will be approximately feature-equivalent to 0.9.15 but work only with Python 3.5 and higher.