The REW Leads App is a 1-1 relationship, but you can logout of one and login to another. It would probably be much easer though to just use the REW CRM which is fully responsive. Just save each /backend to your phone, assigning is super easy from the dashboard, just select the agent and click “assign” (it then clears that lead from your dashboard as it’s already dealt with.
Also if you’re super admin for each site, you should get an email that notifies you about each lead, just click that and it should take you right to the lead record to assign it. Just click assign agent on the right hand side, grab and agent and assign.