Firstly v11.x was based on Ubuntu; since v12.0 TurnKey has been based on Debian so there is no OS level upgrade path. Back in the day, the migration from v11.x to v12.x was pretty straight forward using TKLBAM. However as we haven't supported v11.x for a number of years TKLBAM is not an option.

Also there have were significant changes between the version of Django included in v13.0 and v14.0; let alone all the way back to v11.x! Even if you could use TKLBAM I am almost certain that you would end with a broken webapp anyway...

So I see 2 options:

Investigate and implement a manual migration for your current Django app to the current v14.0; or

Use TurnKey core as a base and manually install a similar version of Django to what you have currently and then manually migrate your Django app to that

The first option would be the preferable and far superior one IMO but will involve the most work. The second would still involve a bit of work but the migration of your data/app would be much smoother. The downside will be that the version of Django you install will probably not be supported (or will end support very soon).

Which way you go (or whether you choose something else) will probably depend on your current usage and you longer term plans for your Django app. If you are only using it locally then your app's security may not be such an issue so option 2 may be best (or maybe even leave it as is if you have some other method of backup). If you already had plans to do some major works on your Django app sometime soon then waiting and doing option 1 at the same time would make sense.

There may be other options that I am missing but I don't think so...