LSI

Will the real LSI
please stand up?

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Yes, it's this one! (well, almost)	Yes, it's this one!
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"LSI" has two meanings:

1. In-game, it refers to the "LSI tracker (and harness)", a set of two items that Konoko must collect in order to place a beacon on Muro's VTOL in Chapter 5. You did talk to this guy, right? He's the only one who calls it a tracker and harness; the objective text mentions the Rappelling Harness as a means to reach Muro's plane but says nothing about a tracking device.
2. "LSI" is also an acronym for "Level Specific/Special Item", referring to a story-related item that you pick up in a level which gets added to your inventory and allows the mission to progress. Oni only supports one special item per level and only five missions take advantage of this feature. One of the five special items is the "LSI tracker and harness", but from an engine standpoint they are all termed LSIs.

You can read about each of the game's LSIs starting HERE. You can learn how to give them to the player in a script HERE.