Should you apply leather conditioner to block strop? I have watched several videos of people making block strops and no one mentions leather conditioner.
I use Naniwa blocks with diamond paste - you use very little of diamond paste, so it doesn't have enough oil to lubricate the leather. Might be simpler with the usual compounds. Anyways, after a while, when the strop has become loaded with abraded metal, I use leather cleaner to remove all the stuff. The leather cleaner is somewhat aggressive, so the leather can become quite dry and brittle but also very clean
So I add a bit of conditioner to it, and that seems to work fine. Just not too much, otherwise the leather will be too soft and saturated.
Haven't tried it any other way, there is probably a simpler way, but this works as well.
For my razor strops I like to use Collinite Leather wax. It is a mix of conditioning oils and wax. Buffs to a smooth slick shine that helps the razor slide well. Not so important for knives and would not work well on the suede / nap side of leather.