(Some of this is rather elementary, and is not intended to imply that you don't know it, it was just part of me getting to the conclusion.)
If the top chord is straight and in compression, it will bend laterally at some load if not restrained. For a pin-connected truss, the member would need to be designed for an unbraced length equal to the effective compression length of the chord, for the axis which is free to move. This may be longer or shorter than the physical member.
Where the continuous truss has intermediate support, the top chord force varies from tension to compression, but the structure is indeterminant and this whole scenario goes out the window as live loads move across the truss.
I recommend running appropriate models, making sure to model the joints as fixed, since this design looks like it will be functioning as a hybrid vierendeel truss, so typical truss rules are not effective. This will tell you what length, if any, is in compression. [Intuitively, I think that with only self-weight, the bottom chord will be in compression at the supports (B', C', 3, 4?) and the top chord might have a little compression near midspan with live loads applied, if I'm looking at it correctly.]
The vertical members appear to restrain local twisting about the top chord member's axis, which would prevent LTB. But you can only use the vertical member to resist a lateral-only buckling mode to the extent that the structure will resist lateral movement of the chord member.
The degree of lateral restraint provided by the vertical member would be a function of the ability of any torsion-resisting connection at the bottom chord to resist forces presented at the top chord.
Once you determine the force required to resist lateral buckling of the top chord, model the cross section of the assembly to see what happens when the force is applied at the top chord. Essentially, place a sidewards force, equal to the buckling force, onto BOTH top chords, and check inward, outward, and one of each simultaneously and individually on the chords at the same location.
You need to verify that the stiffness of the structure provides sufficient restraint, including 2nd order effects.