Hi Boilatas,
it depends in which coordinate system do you want to have your results. As you have GCPs in Lambert then I suppose your results should be also in Lambert. In that case you can set the Output CS to Lambert in the application settings. Then the results will be in that system.
RealityCapture is capable to work with various CSs, as there are used transformations between them. But if you want to use WGS, it is basically the same. It depends on your need and you don’t have to change the coordinates if you will have set everything correctly (as you want, Project and Output coordinate system). The images are mostly in WGS CS and this transformation is basic. As I wrote, in mostly cases it depends on used GCPs.