I'm working/testing using Firefox (latest rev) on Windows. My code is similar to
....
var lm = new jsts.operation.linemerge.LineMerger();
lm._factory = geometryFactory;
var geom = // Command that produces a linestring geometry type
lm.add(geom);
When run in the debugger, the last call shows an exception. Since I am using the minified code (I can't figure out how to use the base code directly - not really a JS person), I can't see details. Same problem is occurring if I pass it a geometryCollection, and with several of the similar lineMerger classes - all complaining about 'this.add()' call. If it makes a difference, this is buried in an old extJS application that also uses OpenLayers V2.
Let me know what else you need and I'll see if I can provide.