I just bought an eighty-six year old farmhouse with plaster and lath walls. When these older houses were built what kind of insulation would they use?

Probably nothing in the walls. Probably some has been added to the ceilings at some time since the house was built.

I usually recommend to clients that have old houses to insulate the roof/ceiling as much as possible, the floors as much as possible, and take care to seal around windows and doors and other leaky places, and leave the walls until last, if at all.

There is no really good way to insulate a wall without tearing off either the interior or the exterior.

There is no really good way to insulate a wall without tearing off either the interior or the exterior.[/QUOTE]
I'm responding to an old post but it may still be useful to the person that posted the question and others.
I routinely insulate old frame homes that have plaster and lath interoir finish. There are hundreds, maybe thousands of insulation contractors that do the same. As with all things, some do bad work and some great work.

I blow cellulose using a tube that I slide up or down the wall and the material is injected into the wall cavity under significant pressure. My goal is 100% coverage and a "dense pack". Dense pack is defined as 3.5 pounds of cellulose per cubic ft of volume. This is twice the density of what is open blown such as in an attic. Plaster and lath walls are extremely tough. They are the only walls I never worry about "blowing off". The cellulose is packed into the wall tightly enough that it will not settle and so that it drastically slows the air leakage the flows through the walls. I use infrared and air leakage testing equipment to quality control my work.

Every house I do has a significant reduction in air leakage and fuel bills. There is the added bonus of sound control. I access the wall cavities by removing the siding and drilling through the sheathing that's under it. When the siding is replaced, the only evidence that the work was done is the chipped paint on the siding that was removed.

At todays fuel prices the energy savings usually pays for the cost of the work in 3 to 4 years.

Obviously, I disagree with the quote!
Steve/starbrightEnergyServices/Wellsboro