Lapang, facing revolt by at least 14 legislators, is expected to tender his resignation to Governor R S Mooshahary later on Monday after he returns from New Delhi along with 23 legislators.
A CLP meeting is likely to be held n Shillong in the evening to elect the new leader.
Another meeting of the alliance partners of Congress is also likely to be held later, the sources said.
Lapang had met Congress President Sonia Gandhi on Sunday evening and apprised her of the developments and offered to quit, party sources here said.
Congress President's political secretary Ahmed Patel, AICC secretary L Faleiro and senior party leader Oscar Fernandes were present during the meeting with Gandhi at her residence where Lapang admitted that he had failed to meet the demands of some legislators.
Lapang also assured Gandhi that he would extend "all support" and help to the new government to be led by Sangma.
Before meeting Gandhi, Lapang had admitted that he has lost majority in the CLP and said he was ready to quit paving the way for his 43 year-old deputy, Mukul Sangma to take over.
At least 21 legislators have pledged "unconditional support" to Sangma.
The 14 dissident MLAs have been pursuing the Congress high command for nearly a month for change in leadership as well as their inclusion in the ministry.
Only six Congress MLAs out of the 28 have found berths in Lapang's ministry.
The current ruling Congress alliance, sworn in last year after the fall of the NCP-led government, enjoys the support of 44 legislators - 28 from Congress, 9 from UDP, two from Hill State Peoples Democratic Party, one from Khyun Hynniewtrep National Awakening Movement and four Independents in the house of 60.
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