Here is the answer I received from Buy me a Pie support for Android...

Unfortunately, it is not possible to change the lists order manually on Android. Besides, there is a workaround: open the list to copy it, choose the "Duplicate" option in the menu. The copy of the list will be transferred to the top. The original list can be deleted.

I emailed them too, and got a confirmation email back that they had received my email and were looking into it.

The lists on my phone won’t slide either way. I compile my lists on my iPad and email them to myself. Maybe that feature isn’t supported on the Android.

Here’s the email where I asked about it (iPad). They replied to me in a matter of minutes...

support@buymeapie.com

But I noticed on my phone that the email address for Android is...

android.team@buymeapie.com

I found this email address buy going into my lists and tapping feedback. It should give you an email to send to them with your question.

Sorry about that. I didn’t realize that this was the answer for the iPad only. Hope the above info helps you find the answer.

I’m using an iPad. Let me look at the app on my phone, and I’ll see if I can figure it out. The phone app is different than the iPad.  Let you know.

The little box  in the upper left corner that denotes the number lists you have. Tap on it, and your list of lists will open. 

I asked this question of support a month ago, and here is the answer:

Tap the lists icon to open the lists manager. Swipe the list title right to left, then tap "Pin top". As a result, the list will be transferred to the top. You can pin as many lists as you wish.