However, it argued the government has no clear strategy or timetable for doing so and called on it to consider making use of self-assessment and national insurance contributions to auto-enrol the self-employed.
This comes as the report highlights the growing concern about the number of self-employed, including gig economy workers, who are not covered by pension auto-enrolment.
Industry has responded with criticism to the call for the abolition of the Lisa with Skipton Building Society saying this would "let down a generation of savers".
The firm called on the government to ignore the recommendation. Kris Brewster, Skipton’s head of products, said: "Originally, the government aspired to see 200,000 Lifetime Isa accounts opened in the first wave of activity.
"At Skipton, in just over one year, we have opened over 112,000 accounts for our members. We believe the Lifetime Isa can make a real difference for people wanting to get on the housing ladder."
Tom McPhail, head pf policy at Hargreaves Lansdown, praised the committee for pinning the government down on its responsibility for long-term household savings and financial resilience.
But although he said the proposal to abolish the Lifetime Isa addressed the concern that the savings landscape has become over-complicated, he warned the Lisa had proved popular among savers.
He said: "The Lisa is proving popular with those who are eligible so we’d want to see a proper consultation process before the government took any steps in this direction.
"A root and branch review and simplification of retail savings and tax incentives would be welcome but is almost certainly beyond the capabilities of this government, certainly until Brexit is resolved."
Laura Suter, personal finance analyst at AJ Bell, said: "The Lifetime Isa has introduced complexity but there is a danger that scrapping it 18 months after introducing it, just as the product is becoming established, would further dent consumer confidence in the savings market.
"Such a drastic move should be considered within the context of wider changes that could help savers."
The MPs advised the Treasury to report on the state of household finances in the next Budget and identify the key risks to the financial resilience of households, and set out its strategy for addressing them.
Phil Andrew, chief executive of StepChange debt charity, who gave oral evidence to the committee as part of its enquiry, said: "The committee’s report shows a clear understanding of the debt landscape, a keen awareness of where problems lie, and a robust identification of who has the power to solve them.
"We look forward to working constructively with policymakers to help them address the problems set out so cogently in the report."