If GHS primary is ok for you, then seems LH is more safe. It will be even more difficult to get into her primary school in future as it has its own KG students.
DSS / private schools' acceptance depends too much on luck (plus interview performance). I've heard from my friends that some v smart kids who get a lot of prizes at school cannot even win a place in those good DSS / Private schools. This might be due to their nerviousness during interviews.
To lower your kids and your stress, better find schools with backup, though ghs is not the very top ones like dgs