The only useful flexible through tickets I can see that permit break of journey are:
Anytime Single routed LNR & WMR only for £77.20
Off-Peak Single routed Any Permitted for £79.80 (restriction 2C)
An Off-Peak Return also exists at £114 if you're returning to Liverpool in the next month.
[Updated - see below]
It looks like the cheapest option is to buy two separate journeys:
Liverpool Lime St to Crewe single is £18.50
Lichfield TV/Tamworth to London off-peak single is £41.20 or super-off-peak single (arriving into London either 1300-1559 or after 1900) is £36.60
The forum site is offering some slightly cheaper split tickets than this that may also be worth looking at.
I can't see any particularly useful advance fares for this split but that would also be an option if available.
-----------
Updated
I've just realised it would be possible to buy a London Euston to Liverpool Lime St super-off-peak return (LNR/WMR only) for £46.10 and discard the outward portion. Break of journey is permitted on the return portion. This would require you to arrive into London after 13:00 and not depart Liverpool between 16:00 and 19:00.
There's also a similar London Euston to Liverpool Lime St off-peak return routed LNR/WMR only for £60.50, which you could discard the outward portion of, and which is valid to arrive at London after 10:00.