Hi William it’s not possible at present. But bear in mind this is an early release of Lightroom for Apple TV. I’m sure Adobe will be bringing forward the kind of features you are looking for in future iterations but for now the actions available via your remote control are limited. Have a look at Scott Kelby’s tongue in cheek FAQ where all the answers are no, including your question. Of course you can view in date or custom order on the iPad or iPhone until the TV version catches up.
Yesterday, a new version of Lightroom TV was released that allows sort options by newest, oldest, or the custom order specified in another Lightroom app.
Please update the app and see if this is an improvement for you.
Charlie, sorry to say that apparently the new update for Apple TV doesn't work. I have a number of collections in Lightroom on my computer in a custom order synced to LR mobile. On my iPad using the custom order selection in the dropdown menu they display properly. But on Apple TV, where I want to view them with friends, the sort order is completely mixed up even when I choose custom order, apparently without rhyme or reason. It was working well with the photos displaying in correct order until this latest update. Can you please provide a fix?