First off, Lateral Torsional Buckling (LTB) is only applicable to beams. Beams are members that are loaded so that they have moment. This is what the first image shows. The members in the second image are not beams. They are struts that are loaded primarily axially. They are holding the walls of the excavation apart.
This means that LTB is not a controlling consideration for the struts as pictures. The rest of this answer does have some portions that would be applicable to both columns (struts) and beams though.
Lateral Torsional Buckling
As mentioned in the question, LTB occurs when the compression flange of a beam starts to rotate out of plane (buckle). Buckling is controlled for LTB of a beam the same way that it is controlled in a column. It is controlled by bracing.
The lacing of two members together effectively makes the built-up member act as a whole. The controlling properties are now the combined section properties instead of the individual properties.
Individual codes might use different equations or methods to check for LTB, but the basic mechanics are the same. The distance between braces on the built-up member is what matters for a given section.
In laced members, the lacing is the smaller bars that go between the main members. This is typically in a zigzag pattern. The lacing is there to tie the members together to make them act as one. For an individual member, the lacing effectively braces it at each location.
The bracing must be designed so that it can transfer shear from one member to the other. In the US, codes require the lacing to be designed for about 2% of the axial load in the build-up member. AISC and AASHTO have limits on the spacing of the lacing connections based on the buckling of the compression flange of the member between lacing points.
Assuming that the lacing is designed as required, the built-up member will act like one section and the individual components do not need to be analyzed individually.
Lacing is not considered external bracing. The lacing bars are an efficient alternative to providing solid cover plates to create a built-up member. Bracing is external to the member as a whole.
In the US, AISC differentiates between nodal bracing and relative bracing. These differ in that nodal bracing provides rigid brace points that do not move, while relative bracing only ensures that two brace points do not move relative to each other. There are different formulae that account for the bracing of a column using each type of brace.
To your question, the individual members will be braced at the 1 meter intervals and, this would be relative bracing. This distance is too far apart to be considered lacing.