The quango, which funds education and training for over-16s, is suing a small organisation in Wolverhampton called Kids in Communication for breach of contract.
Umbrella bodies the NCVO and Acevo are urging the council, which has been trying to encourage more charities to bid for contracts, to drop the case.
They claim the council has frequently abused the Compact and that court action is a draconian approach that could jeopardise the future of Kids in Communication, which has trained 4,000 young people in radio skills since 1999.
They say it could also set a dangerous precedent for the skills body and the wider not-for-profit sector.
"This is seriously not the way to behave," said Stephen Bubb, chief executive of Acevo, who has written to Compact Commissioner John Stoker asking him to intervene.
"The LSC needs to understand the damage this would do to its relationship with the voluntary sector. Taking a small charity to court is heavy-handed. I expect the Compact Commissioner to take this up as a matter of urgency."
Stuart Etherington, chief executive of the NCVO, wrote to education secretary Alan Johnson in January expressing his concerns about the LSC's "extreme action". Last month, the NCVO, which is still hoping to reach a settlement before the case goes to court on Monday, said the skills council had a "bullying culture".
The LSC, which receives £10.4bn a year, appointed nine 'charity ambassadors' last month to tell staff about the value of working with the voluntary sector.
Nicky Brunker, the LSC's head of marketing and communications, said the organisation was "absolutely committed to engaging with third sector organisations". She added: "We have pursued this legal action as a last resort."
Stoker said: "Because this case is now before the courts, it would be inappropriate for us to comment further at this stage."
NSPCC director Mary Marsh, who sits on the LSC's top-tier decision-making National Council, declined to comment. Fellow council member Shirley Cramer, chief executive of Dyslexia Action, was on holiday as Third Sector went to press.