From other devices from the release years 2013/2014 I know of similar stored problems, such as the BlissLauncher, which no longer works correctly. I assume that the “falcon” e-0.7-n-2019111931239-dev-falcon will no longer receive /e/ OS updates and will be discarded as part of the device streamlining.
Since February 2020 there is a monthly updated unofficial LineageOS 17.1 ROM, which was re-released today: lineage-17.1-20200607-UNOFFICIAL-falcon-Moto_G_XT1033 (Note: I’ve not tried it myself and don’t take any liability; using it is at your own risk).
LOS cannot replace /e/ OS for the Privacy & Security items, but it works with current security patches.
By the way: For testing purposes, the /e/Apps Store works for me with LOS 17.1 and more …