Would you describe this setup a bit further. Does this mean that you're generating the code with T2L and then cross-loading it to the Lw3?
I'm not using T2L at all. Laserweb3 is a complete software that runs on any machine (Win, Linux, RPi etc). Laserweb3 can control the machine and generate gcode from SVG, DXF, BMP, JPG, etc etc (basically most vector and raster formats) AND also serves a web interface. So it's not accessed like normal software that is run locally on a machine but it's accessed via a browser.
You connect the USB from the laser to the raspberry pi and run the Laserweb server software on the RPi. Because the RPi is serving the interface, you can access it from a browser on either the machine it was installed on (eg localhost) OR any other machine that can access that server location over any LAN or WAN network.
So in for my setup, the RPi is connected to the laser and running the Laserweb3 server. Then on my PC I open Chrome and connect to it over my LAN network (eg. 192.168.1.100:8000) and then just drive the software and the laser from that PC. Both my RPi and the PC are connected to my home router via WiFi.
Once it's set up, it's really easy to use and it frees up my PC from having to be tethered to the Laser. Hell, I have even sent a job to it from my phone using it's browser. You don't need any other software to drive it - just over the browser. The project is a work in progress and has some quirks but is quite capable already. If you wanted to, you can also just load Gcode from other software and just use Laserweb to control the machine and run gcode. It's up to you what you do but it is supposed to be a one stop shop type software.