The whole Allerton-Hunt's Cross area sorely needs improvement. I'd suggest making use of the width of.the formation to install 4 tracks (if necessary, taking a bit of land from the depot), 2 for Lime Street-bound trains on the north side, and 2 on the south for Merseyrail trains terminating on the south side at Hunt's Cross (with a crossover to the east to enable them to turn), and 3 / 4 tracks continuing as far east as there is space for. Sadly, any of this will probably have to wait for CLC electrification, which will.probably fail to address the problem completely and set the conflicts at Allerton in stone.
Simplest thing they could do is stop the conflicts with Merseyrail crossing over at Hunts Cross. At least then the CLC trains s could then have a better approach upto Allerton. Still needs serious money but it seems an obvious quick win.