Yes, you're reading that right. Once the cross-sign expires, Android prior to 7.1.1 won’t work out of the box with Let’s Encrypt.
If you are an application author, you can include the Let’s Encrypt root in your app, and users will have to upgrade.
If it’s your device, you can install the Let’s Encrypt root. Or for websites, you might be able to use an alternate browser like Firefox Mobile which ships its own set of root CAs. Or upgrade the OS.
If you’re a website operator, you may have to switch CAs.
I've posted a solution on stack overflow to get Android clients whose trust store is out of date working again. I implemented it a bit empirically, without being sure that what I was doing was the right solution. Could someone give me some feedback? Is my implementation correct? Won't there be another problem in the future? Thanks in advance for your help.
Please don't include intermediate certificates, only root certificates. See e.g. New Intermediate Certificates - Let's Encrypt where Let's Encrypt writes how the usage of the intermediates is going to change soon.
If those Android versions support ECDSA, it's better to include ISRG Root X2 next to the X1 root you already mention.