FYI don't use Lemmy DMs to discuss anything sensitive. It is not a secure chat. This is why we have the option to put Matrix contact info on our profiles
At the moment it don't seem like it's supported in this app. But Lemmy has this supported and if you use other apps like Voyager you can send messages to other users.
And yes the app supports messages in the inbox but I've yet to see an option to send messages to users I'm afraid.
Hope they will implement it soon. Note that the dev of this app is the same as the lead of Lemmy and it might take time for them to update it as he has his hands full with Lemmy as well.