The formal impact assessment, issued as the Savings (Government Contributions) Bill 2016-17 receives its second reading, showed that the government expects 200,000 people to save in a LISA in 2017-18 rising by 2020-21 to in excess of 800,000.
The average contribution for the 2017-18 is expected to be £3,500, which would make the LISA market to be worth £700m in 2017-18.
Only a negligible impact on the pensions system is expected, with a saving of some £10m in tax relief as investors move from personal pensions to LISAs.
By 2021-22 the exchequer would face a £850m cost paying the LISA top-up.
Hargreaves Lansdown head of retirement policy Tom McPhail said: "The LISA will undoubtedly prove popular with those savers who want the flexibility to save for the long term, benefit from the government top up but who also want to retain access to their savings."
He said the assessment had shown it would "make sense for the government to press ahead with the launch of the Lifetime ISA, especially as we know ISA providers will be ready to meet investor demand in 2017.
"However in the longer term, there is clearly more work to do to tidy up the increasingly messy savings landscape for investors."
Mr McPhail called for all ISAs to combined in one 'super ISA' and for pension tax relief to be simpler, fairer and more cost-effective system.
The LISA allows users to save up to £4,000 each year, and receive a government bonus of 25% which can be used buy a first home, or kept until age 60 when savings may be taken out tax free.