As people seem to be pretty curious about this idea, I thought I'd set out what I mean by it in some detail, if for no other reason than I think it would make a good talking point!
First of all, I am not proposing endless number crunching or Lara gaining levels of experience or anything like that. Those are often used parts of RPG systems, but they are not an essential part of what makes an RPG.
RPGs are, in essence composed of three things: story, characterisation and player choice (Yes, JRPGs and ARPGs are something else, but bear with me!)
What I would like is to incorporate the essence of choice, as well as bringing in a few more elements from normal RPG systems, such as a proper inventory.
Lara has always had an inventory, but despite the backpack she wears everywhere, it's always been a bit basic. I'd like to be able to change weapons and outfits from within the inventory, allowing Lara to switch weapons or outfits as the player desires.
This would allow Lara to carry more weapons, as in the older games, and allow picked up outfits to be found within the game itself. Because there would still be buttons for things like using health packs, the interference of the inventory with game play would be fairly minimal, for those who are not keen.
Allowing for more inventory items also allows for new types of challenges, of course. Different outfits could be more effective in different areas (Heavy Arctic gear, swim wear, etc). Wear a bikini in the Arctic, and you'll freeze, etc.
The choice element comes in with conversations, of course. Though most of Lara's adventures do take place in isolation, there are always times when she talks to someone. Having dialogue options would help the player play Lara the way they see her.
It may also be interesting to give Lara a choice of routes (As was done with TR3. A very good idea, in a not very good game).
Other possible choices could involve things like 'shoot bad guy who is begging for mercy' or 'spare bad guy who is begging for mercy'. A situation Lara sees a lot! Both options could have consequences down the line, and not always as expected.
So I'm not really proposing to re-invent the wheel, here. Just deepen certain aspects of the game that have been there all along and give the player more choice in how to play 'their' Lara.
This is what I think AoD was on the edge of achieving. If they hadn't put in the silly push specific block stuff and actually finished the game before releasing it, I think it may have been the closest TR game yet to what I am proposing.
What are your thoughts, ladies and gentleman?