Firstly there are perhaps a dozen LC frequencies. The other thing is that LC won't talk to you unless they can see your tail # on their computer, and for that to happen there has to be some prior coordination.
How this works is a mystery to me but you have to get a squawk allocated initially, which has to be out of the right range of numbers for LC. I don't know if that squawk comes from Eurocontrol, but logically it might. Then, in some countries (not the UK, apparently) as soon as the radar picks up that squawk, your tail # and flight planned route pops up on the IFR controllers' terminals along the route. Then when you call up the IFR controller, you get a response right away (in seconds, with LC, who often ask for a squawk ident to make sure).
If you have not been allocated that "right" squawk, LC will never offer you a service (because they can't see you) and this is one reason why some pilots find they cannot get into CAS in the UK - the departure tower has given them a wrong squawk to start with. This happens every time if you file IFR in the UK but at a "low" level e.g. FL060 OCAS e.g. Lydd to Cardiff.
This is about all I understand, and I have found it very hard to find anybody who can fill in the detail.