Borum, R., Fein, R. & Vossekuil, B., A dimensional ap- proach to analyzing lone offender terrorism, Aggression and Violent Behavior (2012), doi: 10.1016/j.avb.2012.04.003

In press, but available now, here:

http://www.sciencedirect.com/science...59178912000432

At its core, the paper identifies three dimensions of lone offender terrorism, and notes that in each case these dimensions will be present along a continuum. The following is derived from a figure in the draft study:
Loneness (Degree of independence of action)

From: Offender initiated, planned, prepared for and executed the attack without (direct) assistance from any other person - SOLO

To: Offender initiated, planned, prepared for and executed the attack with (direct) assistance from one or two other people - LONE
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Direction (Degree of autonomy of decision-making)

From: Offender received no personal instruction or guidance concerning whether to attack, which targets to select or which means to use from any known member of an extremist group - NON-DIRECTED

To: Offender received some personal instruction or guidance concerning whether to attack, which targets to select or which means to use from any known member of an extremist group - DIRECTED
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Motivation (Degree of clarity of causation/purpose)

From: Offender did not communicate - and it was at least unclear - that the attack was significantly motivated by a political, social, or ideologically based grievance, not by revenge or other personal motives - NON-IDEOLOGICAL

To: Offender’s attack was significantly motivated by a political, social, or ideologically based grievance, and not by revenge or other personal motives - IDEOLOGICAL
That's on top of dispensing with "lone wolf":
Despite its popular use, we suggest avoiding the term “lone wolf” because it carries the potential to glorify or to imbue an image of power to attackers who are otherwise powerless and often ineffectual.
Not to mention addressing the issue of mental health issues:
...knowledge that the subject has a psychological problem or mental illness, by itself, does not necessarily change the level of threat. Mental illness is not necessarily a “master motivation”, nor does it automatically suggest a greater or lesser hazard. We have learned from studying other forms of targeted violence that even subjects known to have mental illnesses are sometimes capable of rather sophisticated attack planning. The operational questions pertain more to the subject’s degree of personal organization than to whether he (or she) has a specific disorder or diagnosis. Mental illness and a high degree of personal organization should not been seen as mutually exclusive.