[Xiaomi Redmi 4X ROMs, Kernels, Recoveries, & Other] SebiderSushi:
TL;DR: Unless you have specific reasons to choose 15.1 take the latest release possible. Especially as the last LineageOS 15.1 build is from Q3 2019. For example, someone once asked specifically for the last lineage 15.1 build because apparently Android Auto works with that.

I suggest to always flash the most secure ROM that works as a daily driver. That is, your ROM must enforce SELinux, should really be signed with developer keys and include as much security patches as possible. SELinux status should be displayed at the bottom of the about phone screen. On LineageOS you can look in Privacy > Trust. To check the signature you need a tool to view X.509 Certificates. It should be enough to check the file META-INF/com/android/otacert inside the ROM flashing ZIP file. For example if it is issued & verified by "Android", expires at "17.07.2035" and the certificate fingerprint reads 61 ED 37 7E 85 D3 86 A8 DF EE 6B 86 4B D8 5B 0B FA A5 AF 81 then it is definitely a public key and should be avoided.

Other than this just look for the ROM with most stability and best device support. For the devices i have used in the past (the OnePlus X and the Redmi 4X), ResurrectionRemix always had the best device trees while LineageOS usually had some issues with hardware support. For example the official LineageOS builds for the Redmi 4X had problems with the fingerprint & a very long delay when taking photos while i last tried them out.

Unfortunately, LineageOS, Lineage4microg, /e/ OS and OmniROM are the only ROM distributors that i know of who have consistently paid attention to enforcing SELinux and signing with developer keys. Those are fundamental parts of the android security model and while taking care of SELinux can take quite some work, seeing ROM Developers release roms that do not enforce SELinux or sign with proper keys really makes you doubt that they sufficiently understand what they are doing.

So yeah it's a tradeoff between usability, stability & security. You can hardly get out of that unless you compile yourself, potentially putting in a lot of additional work, get a newer phone or get another phone with a good LineageOS device tree or better custom rom support overall like the Pixel devices which are usually the main support group of security focused android distributions like GrapheneOS.

Why is this important?​

Simply put SELinux is an advanced permission managent system that can be used together with Linux operating systems. The android security depends on SELinux so much that there are even exlpoits that work as soon as you turn SELinux into permissive mode and nothing else.

The takes of John Wu & the LineageOS team on this topic:

https://twitter.com/topjohnwu/status/1318843385487093760

https://twitter.com/LineageAndroid/status/1365603869493919748/

Regarding signatures:

When installing an upgrade to an android application the system verifies that the update is signed by the same key as the version that's already installed. This ensures that any update must come from the same source. This is important because an updated version of an android app will inherit all permissions the previous version had and get access to all of its data.

During the android development process security is not necessary and only a nuisance while debugging so the AOSP source code includes pre-created signing keys that are used to automatically sign every system app. Since these keys are public, anyone can use them.

This is obviously a problem: If the apps on your ROM are signed with this key, someone could publish a malicious application that installs as an upgrade to your Contacts app, System Settings or your WebView and exploit all privileges these apps have. Now they only have to convince you to sideload this application on your device.