When you talk to hard-core project managers, one of the tell-tale signs of their 'school' of LPM is what language they use to describe their process and one of the hardest things for some PM's to acquiesce to is the short-comings of their school. From my experience, there's no perfect PM methodology, each has great characteristics, but each has flaws. The ideal LPM program is derived not from one methodology (PMBOK, Scrum, Agile, Waterfall, Prince, etc), but by cherry picking the best from each.
Once you've done that, you'll need to consider how to apply to your new LPM methods, taking into account that different types of matters will require different levels of LPM rigor. Adding another layer of complexity is that once you've defined what level of rigor is attached to each matter type, you'll likely have to factor in 'modal LPM', for lack of a better phrase. This is to say that even within a given matter, you're going to need to further refine your LPM efforts based on matter velocity - you'll need to have different modes for different phases of a matter. For example, perhaps you're working on a litigation matter that is going to last a couple years. You may reach phases where the case is somewhat dormant and meeting monthly might be perfectly acceptable. But, at certain points, you may need to transition into what Scrum practitioners refer to as a "Daily stand-up." Key point is to be flexible in your approach, but base your flexibility on a foundation that allows for that.