Updating the firmware of a 3d printer is generally more complicated than it sounds, and isn’t generally going to provide a connection fix like a firmware update for a computer motherboard might. Think of firmware for a 3d printer as generally something that will change your printing paramaters and occasionally add new features, but its much less about bug fixing than other devices might be.
If your computer is driving the printer, it’s more likely that the computer itself is the source of the pauses. if you are driving off the SD card, either a corrupt SD card or a heat issue in the controller box is likely the issue.
You can upgrade with the precompiled lulzbot versions, but going with the taz 6 firmware for example would require you to disable the auto bed leveling and change a few bed parameters. You can upload a custom version using the Arduino IDE and compile it yourself and change configuration.h and whatnot to match your printer configuration. The extruder esteps is going to be different for each printer, and things like the Z steps often change from model to model with different leadscrew hardware.
If you are running a windows computer, make sure your power settings are set to “high performance” and the USB ports are set to “Never Sleep”