Parents are free to apply to schools outside their home county. After visiting schools of interest and deciding on your preferences, the next step seems to be the admissions process for the county in which you live, e.g. Lincolnshire
The City of Peterborough Academy, Special School is a state school for pupils aged from 4 to 18 See: website
Heltwate School is “a co-educational special school for children and young people aged 5 to 19 years with Moderate to Severe learning Difficulties,
Autistic Spectrum Condition and many additional medical needs”. See: website
Marshfields School is “a mixed, day, community special school. We cater for 170 learners aged from 11 to 19 each of whom has a Statement of Special Educational Need, primarily for moderate learning difficulties”. See: website
The Phoenix School is a special state school for pupils aged from 2 to 19. See: summary school website They say,
“At the Phoenix we look at the whole person, planning realistic programmes to meet the intellectual, social, spiritual, moral, cultural, physical, emotional and therapeutic needs of each pupil”.