Since you're doing asynchronous serial communication, you do need to wait for data to come back. You don't know how quickly you'll get a response. Just waiting a fixed amount of time isn't the best solution, especially when you have to tune it depending on which machine is responding.
Look at the example serial VIs that ship with LabView. They show a couple of different ways to wait for data.
LabView <-> Serial.vi uses a loop reading Bytes at Port to wait for data.
Serial Read with Timeout.vi programs a timeout which specifies the maximum time to wait: if data comes in sooner it reads it.
To find the serial examples, from any LabView window goto Help >> Find Examples >> Search then enter "serial" in the box labeled Type a keyword to find:.
P.S. You said you
used a timer to wait for 137 ms. What function did you use? Have you seen the Wait (ms) function on the Time & Dialog palette?