I am surprised that no one replied to your question. OK, not really. You see, there is some liability in answering your question. I am certain that the professionals from ADJ would suggest you NOT attempt what you appear to be planning. I suspect that they have not done any safety testing of mis-matching LTS components...thus they would not want to encourage an application to a customer that might cause damage or injury.
But as a purely non scientific exercise, I found your question interesting.
I just checked the owners manual for the LTS-50T system AND I went into my storage and checked the actual dimensions of my I Beam truss sections AND I also checked three of the lighting tripods I own from three different manufacturers including the American DJ stand that came with the I Beam Truss pieces.
All of the "top vertical pole section" (the smallest of the three telescoping pole sections) as well as the "T top" horizontal poles AND the horizontal poles that form the top and bottom of the I Beam Truss have an outside diameter of 1.5 inches more or less. All of those components have the same diameter of 1.5 inches...more or less. This is NOT the outside diameter of "speaker stands"...it IS the outside diameter of the lighting tripod's top section and the T Top and the I beam truss.
HOWEVER...
...even though the size is "close enough"...that does not resolve your issue.
Your question was "what if" you took three of the 5 ft I Beam extensions...well, HOW WOULD YOU CONNECT THE EXTENSION TO THE VERTICAL TRIPOD POLE???
You see, the extension does not come with the "Slide Mount T-Collars" necessary to connect the extensions to the lighting tripod...they ONLY come with the Beam Connector parts necessary to connect to another I Beam truss section.
I believe you can order the necessary "Sliding T-Collars"...you would need two for each lighting tripod...four in total.
The ADJ part number is "Z-LTS-T". You need to contact your local dealer or contact ADJ directly for pricing and availability.
I am NOT affiliated with any retailer nor with ADJ. My reply above is simply my opinion unsupported by any communication with a professional in this area...in other words...my opinion is worth exactly what you paid for it. $0.00 I accept no responsibility if you patch this together and it falls on something or someone causing damage or injury.
Disclaimer: I am not an engineer and I did not stay in any motel last night. Non professional making random comments with no supporting documentation. Void where prohibited. Do not try this at home. Trained driver on closed course. Contents may have settled during shipment. Objects in rear view mirror closer than they appear. Erections lasting longer than 4 hours, seek medical treatment immediately. Opinions may not reflect the host and management of this forum. Meant as an amusement. Must be 21 to enter. Must be this tall to ride this attraction.
I hope the information I provided helps more than it confuses or harms.