How do you dissolve a business partnership when you have no formal partnership agreement, just a business lease agreement that will expire soon?

Technically the loss of any one partner is a dissolution of the partnership.  No term was specified by the partners but a court would imply a one year term (the lease) followed by an at will term.  Any partner can leave the partnership within the first year wrongfully, or after the one year term (not wrongfully).  You should all wait until the one year term expires, divide profits and capital according to contributions, dissolve the partnership--and have whoever wants to start an new partnership do so.

I would get a written agreement between the parties in regards to the dissolution of the partnership and that writing should state the value of the business, the individual shares of the partners and their payouts at the winding up of the business.  Any other agreements to buy one another out and keep equipment, start a new partnership without the silent partners, etc. should be separate.