Wood – Do lag bolts need to be centered

When the two members are not touching, the bolt starts to act as a "cantilevered beam" (as you have alluded to) and you hit a point where it is not the shear value that governs, it is the moment (bending). You get additional support by the cleat trying to go down and into the wall which puts withdrawel load on the fastener effectively adding more support using the tensile strength of the fastener.

As a note standard zinc hardware store bolts are ungraded steel usually with no actual values assigned to them.

First, if you have the time, you might try to buy some graded bolts online or from a local supplier; not necessarily a high grade, just graded at all so them meet a minimum requirement for strength. Or use structural screws such as Simpson SDS screws.

Secondly, if you have effectively 1-1/4" of cantilever, I would recommend slightly more embedment into the stud. If you hold things flush to the wall with only a 1-1/4" cantilever, I would up the embedment to a minimum of 2-1/2" or more to ensure the wood stud does not crush at bolt under load due to the multiplying effect of the cantilever. Visualize a 12" long bolt embeded 1" in to a 2x4, the wood crushes on the 2x4, the hole enlarges, and the bolt comes out; the bolt does not necessarily even bend before failing. An increased embedment also increases the amount of withdrawal load the fastener can handle when it slides down the wall (if the bolt does bend) and tries to pull out.

Another option is to simply get more fasteners per stud. You can do this by upping the size of the cleat to a 2x6 and use two or three bolts. Or you can add a vertical member below the cleat at each stud and effectively add a bolt every 4" or so in the vertical member with predrilled holes plus the bolt(s) into the cleat. Key is more embedment and/or more bolts to handle the cantilever.

Or, just build them free standing.

The bigger question is how many vertical supports and how long are they? 1/4" lags 2” into the 2x4 has 510lb pull out strength (255lb/inch) put 2 or 3 in each piece of strut and each one can handle hundreds of pounds. 5/16” lags 266lb/inch; 3/8"lags 305lbs/inch. You don’t need a very big lag bolt when using multiples. My examples have a small safety factor added in and these won’t degrade the strength of the 2x4. I usually drill pilot holes, But not all brands of screws need pilot holes. The depth into the wood is the threaded part that provides the pull out strength over ½" sheetrock I would make sure to have at least ¾" -1” smooth shank that provides the sheer strength as the weak point is the start of the threads.