Further education leaders have claimed this is due to government funding running out for apprenticeships.
Since 2014, local authorities have been required to find an education or training place for all 16 and 17-year-olds after they finish their GCSEs.
This can include studying A-levels, starting an apprenticeship or work combined with training.
Department for Education figures show that in 2018, Lancashire County Council gave 91.5 per cent of its 25,280 school leavers suitable offers of education or training. That leaves 2,149 teenagers who could be missing out.
Of those, for 126 the offer was not considered appropriate, usually due to personal circumstances, and 253 received no offer.
A further 1,770 teenagers did not have their situation recorded, possibly because they were not contacted by the local authority, or they moved address.
Association of Employment and Learning Providers chief executive Mark Dawe it was “scandalous” that the Government cannot guarantee funding any more apprenticeships for school leavers.
“The DfE’s most senior civil servant told a Commons committee on Monday that the big issue is that the apprenticeship levy is running out of cash and that hard choices have to be made.
“But the easiest choice is to safeguard apprenticeships for the youngest, many of whom come from disadvantaged backgrounds.”
A higher proportion of 16 and 17-year-olds were made offers by Lancashire County Council last year than in 2017, when 89.5 per cent received a suitable training or education place.
Lancashire handed out fewer places than councils across the North West on average, where 95.9 per cent of pupils received a suitable offer.
Across the region, more than 6,000 teenagers could have missed out on education or training in 2018.
A DfE spokeswoman said: "This year’s September Guarantee data showed that almost 95 per cent of 16 and 17-year-olds in England received a suitable offer in 2018."
She added that a teenager who does not receive an offer will not always be missing education or training.