The honest answer on Lyndhurst schools is that the village handles the little ones and sends everyone else on a journey. There is an infant school in the village itself, St Michael and All Angels Church of England Infant School, sitting by the church that gives it its name. Junior and primary options are spread out across the surrounding villages. Secondary school means a proper trek, close to an hour by public transport or about twenty minutes in the car. Small children walk to class. Teenagers commute.
For the primary years there is choice, so long as you can drive to it. Names in the wider area include Abbotswood Junior School, the Foxhills infant and junior schools, Marchwood Junior School and Calmore Junior School, alongside a run of Church of England infant schools at Copythorne, Netley Marsh and Bartley. The typical primary sits around a quarter of an hour away by public transport, or roughly twenty-five minutes on foot for the postcodes furthest out. In a forest that spreads its houses thin, none of that is unusual. The school run here is a genuine run.
Secondary schooling is where the geography bites. The nearest options are Hounsdown School and Testwood School, both well outside the village, which is why the secondary journey stretches to close to an hour on the bus against about twenty minutes by car. For families with teenagers and one working car, that timing is the thing to plan around, not an afterthought.
Beyond the mainstream there is a scattering of specialist and small-scale provision in the area, including Coxlease School, Forest Park School and the New Forest Small School, which cater to particular needs rather than the general intake. They are worth knowing exist, but they are not the schools most families will be weighing up.
A word of caution that applies everywhere and gets ignored everywhere. Living near a named school guarantees you nothing. Hampshire allocates places on catchment and distance, and catchments move, oversubscribe and redraw themselves without warning. A house advertised as being in a school's catchment is a house near a school, which is not the same thing as a place in it. Before you buy on the strength of a particular school, check the current admissions arrangements against the exact address, because the offer letter in March does not care what the estate agent told you in October.
The schools around Lyndhurst do not come with a headline rating that makes the decision for you, so the choosing is left to you and to the distances. Read the current inspection reports for any school you are serious about, because those change, and the version in someone's memory is usually the version that has already moved on.
The schools here are ordinary, and ordinary is not an insult. What sets Lyndhurst apart on education is not the quality of any one school but the length of the drive to secondary, and that is the part to sort out before you sign, not after.