Two extremely territorial birds with aggressive tendencies... best not allow contact for both their safety.
You could still house them in the same room so they can interact verbally, just be sure they are not approaching each others cage during flight time.
Also, as you have having issues with your LB and suspect some sort of parasite, be sure these birds do not enter the same room until you have visited a vet to rule that out. Be sure to wash hands and change your shirt between interacting with each bird.