Generally LT connections are strictly point-to-point - so an initiator can call a function in a target, one at a time. As you say, in LT one initiator can only make one function call, which must return before it makes a second function call.
If you have two consumers, they must have some routing in-between. The initiator calls b_transport in the router (point-to-point); the router inside its implementation of b_transport must interpret the address, call b_transport in the appropriate consumer, and wait. It cannot return to the original initiator until the downstream consumer had returned.
There's a comment in the 1666-2011 standard
"Although the initiator thread may be blocked, another thread in the initiator may be permitted to call b_transport before the first call has returned, depending on the protocol."
Though an initiator with 2 threads could be regarded as two separate but highly co-ordinated initiators in a sense