I think I have compiled the entire list of available zones. Other coordinates have no zone associations unfortunately so backup may not spawn there but they may come from neighboring zones (I'm not sure). Many callouts do not work in Liberty City (some do, but it's a hit and miss). To be able to use these zones and get backup, you need to add (copy) the region's list in my first post into your regions.xml file located at C:\Program Files (x86)\Steam\steamapps\common\Grand Theft Auto V\lspdfr\data as shown below:
Then, you need to configure your backup xmls to incorporate the "LibertyCity" region into them. This depends on whether you use Ultimate Backup or not but the process should be similar so I will only give the Ultimate Backup version of this. In the DefaultRegions.xml file located at C:\Program Files (x86)\Steam\steamapps\common\Grand Theft Auto V\plugins\LSPDFR\UltimateBackup, there are entries for regions and agencies: meaning in the LosSantosCity region, you can spawn 4 different types of agencies: LocalPatrol meaning LSPD, StatePatrol meaning SAHP, LocalSwat meaning LSPD SWAT, and NooseSWAT. In the LoSSantosCounty region, you will also have the corresponding local (LSSD), and LocalSWAT (LSSD Swat). The state and NOOSE SWAT remain the same of course all throughout the map.
The trick here is to incorporate a LibertyCity entry into each of the LocalPatrol, StatePatrol, LocalSWAT, and NOOSESWAT lists just as you have the same for LoSSantosCity, LoSSantosCounty, and Blaine County. What I simply did was in the LocalPatrol section, I copy pasted the existing LosSantosCity entry of the LocalPatrol Section and renamed the newly pasted duplicate LoSSantosCity region to "LibertyCity". So I had something like this:
Then I took an existing entry from the state patrol section, copy pasted it into the statepatrol section, and renamed it to LibertyCity. You do this for all the types of patrols you have (local, state, SWAT, NOOSE) etc. Since you typically would want the localpatrol to be city units (not sheriffs) to respond as backup in Liberty City, you would stick to copy pasting or duplicating the LoSSantosCity entry only in the local patrol (and only the LSPD SWAT for LocalSWAT in LibertyCity) and changing the region name to LibertyCity.
For the NOOSE swat, you can do the same. Just copy the LoSSantosCity section in the Noose SWAT section, and paste it and change the region name to LibertyCity.
Lastly, you need to do the same for your SpecialUnits list, meaning the detectives and so on. If you want these units to spawn ambiently like they do in the normal GTA V map, then do the same for the LSPDFR xml (the above is for Ultimate Backup configuration, not LSPDFR ambient spawn functionality), meaning go to your agency.xml in C:\Program Files (x86)\Steam\steamapps\common\Grand Theft Auto V\lspdfr\data (or if you use EUP then in the custom folder), and replicate the same process above for each type of unit, meaning transport, local, state, etc ....
All of the above require very good knowledge of xml configurations. If you are not good at this to begin with, maybe it's not a good idea to experiment and mess around.