Classic example of "FPP" fancy-play poker aka trying too hard IMO.

Pre-flop. Perfectly fine defend hand.

Flop- Why are we leading? What are we representing betting into 2 players? What is our plan on the various scenarios that could follow? This is what Dan Harrington calls a "dark tunnel bluff" IMO. We're heading down this dark tunnel that could be dangerous with no real plan. We're out of position and we have very little equity (most likely just four outs). This flop smashes both opponents range also. This looks like a check fold for the most part.

Turn/River- I understand we're following up on our earlier aggression and trying since its the only way we can win. It's just unnecessary aggression in this stage of the tourney IMO. This is a small buy in field and there are surely a lot better spots. We're triple barreling off half of our chips here. 30bbs vs 15bbs is a big difference at this stage.

there are a few reasons why I never lead this spot.

1) when we're defending bb getting this price our range getting to the flop is extremely wide. Even if we have a few nutted combos like A2/22 and some AJ, we have a ton of other hands as well. If we start separating the nutted combos (or even just tp combos) too early then the rest of our range is left unprotected. This means if we develop a betting range (or checkraise range) that includes our best hands and draws then our checking range becomes extremely vulnerable and a target for successful barrels.

2) The opener has all combos of AA/JJ/AJ. I would have almost no AA or JJ here as the bb defender. That's a range asymmetry (hands in his range that are not in ours) that would lead me not to overplay my big hands too early in this spot. You're betting into 1 completely uncapped range and cold call range that probably contains some AJ and possibly some AA. BB has the most capped range.

3) there's a flushdraw on board and we don't have any of that suit. That means ip will have more hands that float as well as hands that raise as a bluff. This would dissuade me from leading.

4) the board is dynamic. Any broadway card, flush card, or jack significantly changes the texture. I generally try to avoid building pots out of position in these scenarios on the flop with a range that will have trouble figuring out what to do on multiple turn cards.

glgl

Of the three players, your range is the weakest on the flop, you should be auto checking everything unless you have a good exploitive reason to lead.

If leading is good on the flop, you'd most likely need to make the assumption that players are overfolding to it, so betting the river is quite inconsistent. You should expect btn's river range to be fairly Ax heavy which is rarely folding at that price on that board.

Theory wise? It's terrible. Exploitive wise? Maybe it's good. But if you're going to assume that a flop lead or flop/turn double barrel is going to be good, then you probably shouldn't be betting this river.