Gmail Auto Suggest Not Working
To fix this, I deleted my Google account from within Lineage OS. I then downloaded the Aroma of Gapps and pushed it to my device. Rebooted into TWRP and wiped cache/dalvik cache and then flashed the new version of Gapps. Aroma allowed me to exclude whichever Gapps I no longer wanted and I then rebooted.

I double checked that both Gmail and Calendar both had permissions to access contacts, but thankfully this process brought back auto suggest.

P.S. there was an issue with contact syncing all the way, whereby I was given the dreaded "Sync Is Currently Experiencing Problems" message. I used the Contacts Sync Fix app in the Play store to remedy this (it worked). It discovered a malformed contact with illegal characters in the notes field (this may ultimately have been the problem in the first place).