The former minister warned that his party risked becoming a "mirror image" of the European Research Group (ERG) of hardline Tory Eurosceptics, suggesting it was "stuck in a trench not moving".
Admitting he was thinking of resigning the Liberal Democrat whip, the MP said he found the current situation "really distressing" and criticised colleagues who "just adopt a position and will not budge from it".
Mr Lamb broke with his party during Monday's "indicative votes" on Brexit to back plans for a softer exit involving either a customs union with the EU or staying in the single market, while the party line was to reject all options apart from a fresh referendum and revoking Article 50.
He was the only Liberal Democrat MP to vote for the single market plan, while only he and former party leader Tim Farron backed the customs union proposal.
The admission that he could leave his party comes a day after moderate Conservative MP Nick Boles announced he was quitting the Tories, saying the party "refuses to compromise".
Mr Lamb told BBC Radio 5Live that he had a "really, really difficult decision" to make, saying: "I've been terribly proud to represent this party in our national parliament for 18 years now but it didn't feel yesterday like the party I know and have loved.
"I've got some big decisions ahead of me but this is really distressing and difficult. I really struggle with people who just adopt a position and will not budge from it.
"It's not the sort of politics that I favour - I favour trying to find common ground. As a liberal I believe in pluralism - different views coming together, trying to find compromise to work your way through it.
"That's what we do in every workplace around the country - surely we should be doing it in our national parliament in the national interest."
In comments that will be seen as a stinging attack on Sir Vince Cable's leadership of the party, Mr Lamb said the Liberal Democrats were at risk of becoming a left-wing equivalent of hardline Conservative Brexiteers in the ERG.
He said: "I don't want us to be the mirror image of the ERG, just stuck in a trench not moving, and that's why I felt particularly distressed yesterday.
"The bottom line is I'm a liberal and I'm that to my core. My judgement is whether I need to resign from the whip of this group but remain a Liberal Democrat."
Mr Lamb said he fully supported local Liberal Democrat activists but felt "a sense of dislocation between me and the centre of gravity in Westminster now".
However, he said he had not made a final decision about whether to leave the party and would be holding talks with Liberal Democrat chief whip Alistair Carmichael.
He also appeared to rule out joining The Independent Group, saying he was more likely to sit as an "independent Liberal Democrat".
MPs rejected all four Brexit proposals in front of them during Monday's votes, leaving Britain's departure from the EU in chaos.
Theresa May chaired a marathon eight-hour cabinet meeting on Tuesday as ministers attempted to thrash out a way forward, with Britain currently on course to leave the EU without a deal on 12 April.
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