The first condition is that both of them can simultaneously bind the virus, so one of them would capture the virus, while the second one would be labelled and must be useful to detect the captured virus. 

If you have a panel of monoclonal antibodies, you may first want to know first to which epitope they bind relative to eachother. This is an experiment that can be performed via higher throughput ELISA in a competitive assay format if you have a sufficient amount of virus and antibody available. The concept is that you coat your virus to the ELISA and detect the virus with a labelled antibody. If you add unlabelled 'competitor' antibody before adding the labelled antibody, it will occupy the binding spots on the ELISA and hamper binding of your labelled antibody. Importantly, you have to add a varying amount of concentrations of unlabelled competitor antibody as the antibody's affinity is as well important. Once you know which antibodies make a match, as in they can simultaneously bind to eachother, the combination can be transferred to the lateral flow assay format. 

@gertrudis Thanks for your answer.