[LG G5 Questions & Answers] Ascii3:
So far, there appears to be eleven custom ROMs supporting the LG G5 RS988. They are:

Resurrection Remix 7.0.2

Based on Android 9.x

Unofficial build

https://xdaforums.com/lg-g5/development/rom-resurrection-remix-7-0-2-pie-t3945626

LineageOS 17.1

Based on Android 10.x

Unofficial build

https://xdaforums.com/lg-g5/development/rom-unofficial-lineageos-17-1-g5-t4039807

LineageOS 16.0

Based on Android 9.x

Unofficial build

https://xdaforums.com/lg-g5/development/rom-unofficial-lineageos-16-0-g5-t3917647

LineageOS 15.1

Based on Android 8.x

Unofficial build

https://xdaforums.com/lg-g5/development/rom-unofficial-lineageos-15-1-g5-t3806842

LineageOS 15.1

Based on Android 8.x

Unofficial build from developer NextDroid

Original thread has been re-purposed for LineageOS for microG 15.1 builds. Thread formerly: https://xdaforums.com/lg-g5/development/rs988-lineageos-15-1-t3781247

Download: https://androidfilehost.com/?w=files&flid=246621

Resurrection Remix 6.2.1

and Resurrection Remix 6.2.0

and Resurrection Remix 6.1.0

and Resurrection Remix 6.0.0

Based on Android 8.1

Unofficial build (From NextDroid, the same developer of the LineageOS 15.1 Unofficial builds)

https://xdaforums.com/lg-g5/development/8-1-0-resurrection-remix-v6-0-0-t3789823

LineageOS for microG 15.1

Based on Android 8.x

LineageOS 15.1 thread from same developer is reused for this ROM: https://xdaforums.com/lg-g5/development/rs988-lineageos-15-1-t3781247

LineageOS 14.1

Based on Android 7.x

https://xdaforums.com/lg-g5/development/rs988-lineageos-14-1-lg-g5-carrier-t3744854

Resurrection Remix 5.8.5 with OMS

Based on Android 7.1.2

Unofficial build (From NextDroid, the same developer of the LineageOS 14.1 Unofficial builds)

No reference thread. Downloads: https://androidfilehost.com/?w=files&flid=260182

Resurrection Remix 5.8.5 with OMS

and Resurrection Remix 5.8.4 with OMS

Based on Android 7.1.2

Official Build (Obsolete. Recommend preference for NextDroid's unofficial build)

https://xdaforums.com/lg-g5/development/unofficial-resurrection-remix-lg-g5-t3507367

AOSPA Paranoid Android 7.3.1

Based on Android 7.x

https://xdaforums.com/lg-g5/development/unofficial-aospa-paranoid-android-7-1-3-t3617643

Nimax Rom 1.0 (Odex version)

Version 2.0 of Nimax Rom is not intended for LG G5 RS988 at the time of this post.

Based on LG Stock Android 7.x

https://xdaforums.com/lg-g5/development/rom-nimax-rom-1-0-h830-h850-t3710841
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EDIT11: Added Resurrection Remix 7.0.2 (Unofficial build) custom ROM to list.

EDIT10: Added LineageOS 16.0 custom ROM to list.

EDIT9: Updated user NextDroid's ROM offerings' details.

EDIT8: Added LineageOS for microG 15.1 custom ROM to the list.

EDIT7: Added LineageOS 15.1 custom ROM to list. There are now two different offering of LineageOS 15.1.

EDIT6: Added Resurrection Remix 6.0.0 (Unofficial build) custom ROM to list.

EDIT5: Added LineageOS 15.1 custom ROM to list.

EDIT4: Added Resurrection Remix 5.8.5 with OMS (Unofficial build) custom ROM to list.

EDIT3: AOSPA Paranoid Android updated and is no longer in beta.

EDIT2: Added LineageOS 14.1 custom ROM to list.

EDIT1: Added Nimax Rom 1.0 custom ROM to list.