magpienga
Yes, it's easily done. Departing Liverpool VFR to the north, leave the CTZ at Seaforth VRP if 27 is in use, or Kirkby VRP if 09. On leaving the zone simply turn right and head off towards the northern end of the LLR.
Now; when to change frequency! If you departed 27 and left the zone at Seaforth I would stay with Liverpool APR until east of Kirkby. Simply because Kirkby is the standard VFR joining point for Liverpool traffic from the north and therefore you'll get relevant traffic information. Once to the east of Kirkby you should advise Liv APR you are leaving the frequency, select 7000 on the box and LISTEN OUT on 119.4 or 119.52. You can if you wish stay with Liverpool APR but a couple of things to remember; we don't have the Manchester QNH and we're probably not talking to any of the other traffic that may be in the LLR.
The standard VFR joining points from the south are Oulton Park VRP (27) or Chester Racecourse VRP (09). You should give Liverpool 5 minutes notice of your intentions to rejoin the CTZ at which point you should receive your joining clearance.
The standard join at Liverpool is not above 1500' Liverpool QNH. Be careful if you are still in the LLR when you receive your joining clearance. You must still fly not above 1250' Manchester QNH until you have left the LLR.
Incidentally, when you ring up and book out on a local detail there's no need to ask permission for this route. Just book out "local" via Seaforth / Kirkby. All we care about is where you are leaving the CTZ, not what you get up to outside it!!