I have a child at one of these schools with a best mate at the other. Both children are doing equally well, likely to get as for most subjects, both are best suited to the schools they chose and both would not have enjoyed each others school...so I would visit both, both on the open day and a private tour on a school day and I will suspect you will get a feel for your child's personality and where they will best fit.
I would say, LSS is better suited to the studious boy, who enjoys reading, happy to take time doing homework, enjoys maths and computing with parents who would prefer him to mix with similar type children/put studies first or a boy who excels in competitive sport i.e. family very involved in county sport e.g. cricket/rugby, they will be quickly spotted and represent LSS at most sports (sporty but not noticed or not at high level unlikely to be picked for teams). All boys so if your child mixes very well with girls at primary (rather than being in the 'boy group', may find it quite hard).
Ashlawn better suited to the clever but reluctant student..not keen on reading/homework, they will do most of their work at school, get pushed to their ability,have fun and lively teachers..but bear in mind it is a comprehensive, so much more diverse (and streetwise) kids), no problems with getting into sports teams (its all inclusive, but be prepared to loose quite a bit!), and a mixed environment diffuses most situations. They are both good schools, but different (but don't get too stressed as all can change at sixth form).