no you are confusing modem mode with modem emulation again, this is why we end up with two different wiring scenarios.
Best way to put this
ATARI,(850,MIO,PR:,Rverter) to (lantronix,modem)
Lantronix to modem
these are wiring
you should be doing this
sio to middlebox (which is proprietary to every middlebox) to lantronix
You can not use pc 9pin assignment to lantronix as your rverter should follow Atari serial assignment if using a 9 pin wire to 25 rs232 pin wire.
The off the shelf 9 to 24 wire in the pc realm are not the same as off the shelf Atari 9 to 24 wires
You can use off the shelf cables from any Atari vendor (they sell both modem and terminal cables)
The pin-out is listed on the schematic you need choose one or the other for your needs.
Your problem sound like you are using a pc9 instead of an Atari 9 in your wiring. The schematic is for SIO to middlebox to modem only