My husband and I signed a lease with a "partner". Due to conflict we want him removed from the lease. The business is in my name but we are "stuck" with the third person. How can we have him removed from the lease and still keep the business?

Did you read the lease? Commercial leases are contracts and all the terms of the partnership should be spelled out in the lease. Does this person have an interest in the business? What type of business (S-Corp, LLC, Corp etc?)

If the business is in your name alone, then the only affect he can have is forcing you to move. The probably answer is you have to buy him out. But we would need to know more for a more definitive answer.

Also, ANY question on law needs to include your general locale as laws vary by area.

I agree, unless he and the landlord will all agree, you just can't remove him