If you're talking about something like a Tele neck pickup that you want to separate the lipstick cover shield ground and pickup ground on, e.g. for four-way switching, you have to do it yourself. Usually.
You can either use a 4-conductor plus bare ground pickup wire (which you can buy from Amazon etc) and re-solder all the connections, just dont use the spare ones. Safer. IMHO is to add the third wire (extra ground) yourself. That way you avoid disturbing the factory solder joints to the very very fine pickup coil wires.
If, again, you're talking about a Tele neck pickup type, you need to break the link between the lipstick cover and the pickup ground, then solder the new wire directly to the lipstick cover.
The best way to do that is to file or sand away the chrome from one of the bent-over tabs holding the cover in place to expose the copper / brass beneath, then solder to the copper / brass. Soldering to chrome usually doesn't work.
Remember also that the lipstick cover ground always goes directly to ground, never through a switch. It's there for shielding, nothing else.