"Do I need a LOTO program on the jobsite?" has a legal answer and a practical one, and they are not the same.
The construction rule. Subpart K's lockout and tagging provision is three sentences. Controls that are to be deactivated during work on energized or deenergized equipment or circuits must be tagged (29 CFR 1926.417(a)). Equipment or circuits that are deenergized must be rendered inoperative and have tags attached at all points where they can be energized (29 CFR 1926.417(b)). Tags must be placed to identify plainly the equipment or circuits being worked on (29 CFR 1926.417(c)). There is no construction-wide requirement for written energy-control procedures, periodic inspections, or locks — the word "lock" does not appear.
Where 1910.147 does and doesn't reach. The general-industry control-of-hazardous-energy standard covers servicing and maintenance of machines and equipment where unexpected energization or release of stored energy could injure employees (29 CFR 1910.147(a)(1)(i)), and its scope expressly excludes construction. A contractor servicing its own shop equipment is in 1910.147; the same mechanic on a jobsite is in Part 1926.
Why contractors use 1910.147 anyway. The hazard — a conveyor, a batch plant, a pump restarting with someone inside it — is identical, and the General Duty Clause still requires a workplace free of recognized hazards likely to cause death or serious harm (OSH Act §5(a)(1)). A written procedure with locks, verification and training is the recognized way to control that hazard, which is why it is the common answer even where only 1926.417 is cited.
On a multi-employer site the practical rule is the host's rule. If the facility runs a 1910.147 program, the contractor follows it; if the contractor's own equipment is the hazard, the contractor brings the program.