You can tell the scenario was written with action movie justification in mind, but even there it fails.
Yes, the bad guy orders his guards to shoot first. But look at the surrounding situation. Lara arranged for a secluded meeting place, went in fully prepared for a shoot-out, intentionally antagonized the guy beyond his breaking point, and arguably even threatened his life. Rather than heroically surviving an attack, it looks more like Lara set everything up with the intention of making the guy attack so she’d have full justification for the following destruction and killing spree.
After triggering a shoot-out in an ally’s place and leaving dead bodies around, with the bad guy having already escaped, she blows up some of her ally’s stuff (and makes a flippant statement about it) and steals (and subsequently destroys) her ally’s motorcycle. (Also throughout Lara is busting open crates to take whatever is inside, regardless of the legal owner.)
She appears to drop a motorcycle from the top of a high-rise building onto the busy street below. This isn’t even the generic crowd endangerment that action movie heroes get involved in with their chase scenes, as the bad guy is already long gone. Lara does this seemingly because she’s too lazy to take the elevator to the ground floor, cross the street, and then use that building’s elevator. She also causes a few more explosions, and potentially knocks some more stuff into the busy streets below.
She then proceeds to kill more armed guards. Yes, it is a Yakuza base, but she’s broken in, is carrying multiple guns, and very likely is firing first. The guards are just trying to do their job in stopping a trespassing heavily armed mad-woman.
Then in the final showdown, when the bad guy is being legitimately honest about the crimes Lara has committed, she quips about how killing his men and taking his stuff is helping him. Even if you allow for the bad guy to be a full on must-be-stopped bad guy, and the guards were all Yakuza criminals, Lara is still joking about killing people who in this situations are only guilty of the “crime” of trying to stop her from breaking in, murdering everyone, and robbing their corpses.
If one of the guards had managed to kill Lara, he’d rightly be a hero who stopped a deranged psychopath’s downtown killing spree.