What are the mechanisms that must be present in order for me to gain lean muscle mass (purely from a training perspective)?
When you look at building more lean muscle mass you must remember the fundamental rules of hypertrophy, which I feel is sometimes forgotten among everything else going on within your training program. There are 3 really key fundamentals which all go towards building muscle:
To illicit a hypertrophic response you need to stimulate the muscle as much as possible, which basically means forcing as much stress via tension as possible with each rep. This is why slowing your rep tempo down builds muscle effectively, because it immediately increases the stress and tension.
The reason this works is because added stress and tension equates to more "NEED" from the muscle, which equates to increased involvement from high threshold motor units (HTMUs). Exciting these motor units is the fastest way to stimulate more muscle fibres which ultimately equates to global muscle breakdown and hypertrophy.
Progressive overload is another key principle of accelerating your rate of hypertrophy, which basically means that over a period of time you introduce extra stress via more weight, more reps or more time under tension. Something which equates to creating an environment where your muscle has NEVER had to deal with these stress levels before.
Periodisation is something which I feel the majority of the gym community fail to utilise which is why they end up plateauing and failing to break past it. It isn't enough to just go into the gym each week and train hard, there needs to be a methodical approach in place to avoid plateaus from setting in.
For instance, different training volumes and rep ranges will illicit a different response and stress on your CNS (central nervous system) which means that by rotating these each week you can avoid plateaus. As a direct result of this you're able to continue growing faster, which makes your training more productive.
Ultimately continuously creating hypertrophy is about understanding the science behind building muscle and knowing how to manipulate these in a positive way.
Note that this is purely from a training perspective and diet isn't mentioned although it is a crucial and very large topic.
Source: Neil Hill, and lots and lots of research from various journals.