I have done similar, but I do not recomend it.
If at all possible, go with Becktho's suggestion of eliminating the other software and just code everything in LV.
I urge this approach because the sharing of the com resource (I believe) is an exercise in futility at best.
If we have to stick with the other software then two extra serial ports and some custom built serial cables could be used to get this going.
Here is what I have in mind.
Com1 > Other software
Com2 > LV recieve
Com3 > LV transmit
Wire the cable such that the transmit line from the device is connected the the recieve line of Com2. In LV copy all data from Com2 receive line to Com2 transmit. The cable should route Com2 transmit to Com1 recieve.
Wire the compliment to tap into the transmit from Com1 >>> Com3 recv >>> LV copy >>> Com3 transmit >>> Device recieve.
When you have all of this in place, and working the original software would talk out it own port have have no idea you are in the middle.
At that point your LV code could insert commands and intercept responses as required.
BUT...
I would not be suprised if you end up having to learn enough about the protocol that Becktho's suggestion will look pretty simple.
Happy wiring,
Ben