A client recently lost a maple to a suspected case of Armillaria root disease. She is reporting that a nearby sycamore is showing signs of the same disease. We would ordinarily remove the tree and roots and burn everything, but due to the location and maturity of the tree, she is willing to try anything to save it - even non-organic options.
Assuming (1) that the signs are indeed of Armillaria root disease (ie the Q to be answered is as the Title) and (2) effective treatment here means of some beneficial impact (without necessarily achieving a complete cure) then according to Forest Insect & Disease Leaflet 78 by R.E. Williams, C.G. Shaw, III, P.M. Wargo, and W.H. Sites:
chemical fumigants, including chloropicrin, methyl bromide, and carbon disulfide, can reduce the infection level.
In general however practical advice is to prefer reducing the stress on infected or at risk trees, for example by dealing with other pests.