I finally got the oscilloscope and made my tests.
This is the tension levels of the LC Technology module (3.3V down to 1.7V):
This is the tension levels of the other module (3.1V down to 0V):
The two modules I tested:
An additonal picture taken during the tests:
After these tests I PERSONALLY got to the conclusion that, as it happend to me, the problem of bayudwirp is in the LC Technology module itself cause it doesn't properly manage the tension levels of the TX pin: it never gives a response cause Arduino couldn't handle the tension levels from the bluetooth module.