Sure there is no reason you cannot connect the R109LH to the internal sounder port on the TZT 3 16F. You will need to get the pigtail cable assembly TZ3-12P-PGT. and splice the bare cable from the R109LH to a 12 pin plug that will go to the transducer port on the TZT 3 display. The only thing you will lose is that the internal TZT 3 sounder is 1kW while the R109LH is capable of taking a 2kW input. That will only be an issue if you need to use the low frequency side in very deep water (over 1500 feet) where the extra power would make a difference. If you find that you have a problem with the deep water performance, you can get the DI-FFAMP sounder box that will boost the power output of the internal sounder to 2kW and use the full rated input power of the R109LH. But I would suggest giving it a try first before spending the extra money. I use a B175L 1kW transducer with the internal sounder and have no trouble at all reading bottom clearly down to 1800 feet. It might read deeper, although the only times I have been in deeper water I was transiting the area and not fishing. I did see it showing water depth over 2,000 feet so it was getting some returns.
The internal sounder on the TZT3 can be customized to allow you to use the R109LH in CHIRP mode or in a fixed frequency mode that you can specify. You didn't say which sounder you were using with the R109LH previously. You may be pleasantly surprised by the performance of the R109LH with the internal TZT 3 sounder.
You may see some interference noise on the display when the DFF-3D and the internal sounder are both transmitting, especially with high frequency. This is easily managed with the interference filter setting on "high." It is also possible to install a "key pulse" cable between the DFF-3D black box and the TZT 3 that will coordinate the transmissions to eliminate the interference. I didn't bother with the KP synch because I did not notice any performance impact from interference filter.