Firstly are you talking about a real lobster, a rock lobster, a crayfish or a large form of shrimp such as Macrobrachium sp., Palaemonetes sp. ?
I would assume as your referring to keeping them with Atyid shrimp eg. Neocardinia/Cardinia/Halocardinia/Xiphocaris sp. That it is freshwater form which rules out true lobsters and rock lobsters and leaves the species of similar form. As you are in lebanon I am not sure on the licensing rules on crayfish but you may be limited in your choices due to invasive species laws and most crayfish are not compatible with atyid shrimp however may be kept with some larger Macrobrachium sp. .Macrobrachium sp. are mainly nasty buggers that vary from opportunistic scavengers to active hunters, out of that species set the most commonly available friendlier sp. is of the Macrobrachium hendersoni genus commonly known as Red claw macro. Palaemonetes sp. are generally friendly and compatible with everything as they are rarely aggressive.