This is almost entirely hearsay so don't take it to seriously, but these are the things I have heard about Lincoln secondaries:
• William Farr has a generally good reputation all round.
• LSST is a results factory and pupil needs are a low priority.
• Castle Academy has been struggling for years - avoid like the plague.
• Christ's Hospital seems to be kind of OK, but probably isn't anyone's first choice.
• Branston is good for sport.
• St Peter and St Paul's is small and cosy, and often overlooked.
• Priory Witham Academy has modern facilities but nothing else going for it.
• Lincoln Minster School (an independent) is nurturing and especially strong in the arts.
• There are good grammars in the county with buses from Lincoln, but obviously they require 11+.
Do you have a feel for where you might want to live?