Consider a split system air conditioner, with an indoor air handling unit and outdoor condensing unit, each supplied with their own 50 volts or greater energy source, and interconnected electrically only by "less than 50 volts" control wiring.

To work on either unit, do you treat each unit separately with one electrical energy source that requires simple LOTO or do you treat as a system with multiple energy sources (including non-electrical energy sources) and use a more complex LOTO procedure?

Depends on the task.

I would say it does NOT depend upon the task.
If you look at it as what it is, Two separate systems, one of which supplies chilled water, or freon, or whatever to the other.

THe air handler end takes a source of "cold" and blows air over it. That source of "cold" could be the "chiller" end or it could just be facility water. Would you shut down the building chilled water pump system, just because you were working on an air handler?

THe LV interconnection is a red herring.

OTOH, if one is the electrical source for the other, then there are some issues.

LOTO falls under at least 5 different sections of OSHA regulations. There is LOTO for general industrial maintenance, Subchapter J, For electrical, Subchapter S. For distribution/transmission/generation which would not normally affect an HVAC system but if it is fed out of the same panel then you work with a combined Subchapter R & S rules., and there are multiple variants of the Subchapter R LOTO rules depending on if it's for instance in an automated or manual substation or at a generating station And if it's construction or the work being done is construction-like, then it falls under 1926. There's also minor servicing and adjustment that falls under Subchapter O,. So at a bare minimum it is necessary to determine whether the work to be done is minor servicing and adjustments, maintenance/repair, or outright replacement. And it is necessary to determine whether or not it is mixed with generation/transmission/distribution equipment. As an example of the differences Subchapter J and S require locks but not tags. 1926 requires tags but not locks. And Subchapter R can be either/or depending on which part applies. Subchapter O may not require anything but requires a written procedure whereas Subchapters J & S as an example require a written procedure but state that simply having a copy of the regulation is sufficient. Subchapters R & S require qualified workers to execute several steps of the procedure whereas 1926, J, and O do not. Subchapters R & S require testing for absence of voltage and possibly temporary grounding but the others do not.

So adjusting a louver or perhaps even changing jumpers (Subchapter O, minor servicing) may not require locks or tags at all. Outright replacing the unit requires tags but not locks (1926). Replacing a fan motor would require locks and testing for absence of voltage but replacing just the fan blade itself requires a lock only. And if the unit is fed out of a lighting panel that also houses controls for a cogen control system, a more detailed procedure with "clearances" and tags and perhaps locks is required.

Moving on to the hazards, the signalling between both units is usually pretty low level and in many cases may not even be a shock hazard, or the shock hazard may be "avoid contact". The fluid ("freon" but could be ammonia in older systems for example) is the bigger issue as far as servicing goes. There's not much pressure in most cases but it can be a health hazard if the line is broken. So again, depends on the task. If the work is only in one unit or the other, then it can be treated as two separate units. But if the work involves the interconnections between the two units (usually plumbing) then it may have to be treated as a single system.

So as I said...very task dependent for an open ended "LOTO" question.

Rule 1: Job hazard analysis. What are the hazards that the employee will be exposed to? That will drive the content of the LOTO procedures.
Rule 2: You have to take purposeful and accidental contact into account.

For a split system you can have two procedures but both are going to have to address the same hazards. My recommendation is to have one more complicated procedure.

MikeCJ