Great question. As Lumberjack is just a layer on top of WordPress, you can register and use custom taxonomies the usual WordPress way.

Saying that it is something we are keen add into Lumberjack. We were thinking of a similar setup to custom post types. We have made a start in this already, but I can't say when it'll be finished.

It's also worth noting that due to Lumberjack's extensibility, you can write your own implementation. You could write your own service provider to register. This is Lumberjack's service provider for custom post types as a guide:

https://github.com/Rareloop/lumberjack-core/blob/master/src/Providers/CustomPostTypesServiceProvider.php

Any more questions please let me know.

Thanks for the great answer. I've managed to implement the registration of custom taxonomies the same way custom post types are registered. This still needs some work, but the basics are layed out at this point.

I'd love to see what you can come up with better and deeper support for taxonomies within lumberjack.

Glad you managed to handle the registration yourself. We have some decisions to make, that involve understanding more about Timber's Term class more, as we'll probably want to extend this (similar to how we extend Timber's Post).

So yeah, this is on the cards but we want to make sure we get it right :)

Is there any news or progress on native custom taxonomy support in Lumberjack?

+1. Just ran into the need for taxonomies. @joldnl would you mind sharing your implementation? Cheers!