I believe that Reach products will be ideally suited for this task. PPS is what you are asking for (Pulse Per Second). Let me refer you to this page in the Reach RS+ docs:
See the electrical specs section (download the PDF file) and that there exists a PPS (pulse per second) output on pin 5.
If you were thinking about using the Reach M+ instead, then go to this page in the docs:
See the connectors pinout section and that there are dual PPS outputs at C1 and C2.
Now, on page 9 of your Livox user manual, notice that the input type is RS485. Reach RS+ and M+ output the PPS signal as TTL-level UART. You will need a signal converter to interface them. Search using the two keywords “RS485 UART” and see a plethora of signal converters available; some as cheap as $10.
On page 16 of your Livox user manual is a description of the PPS synchronization logic. According to that description, I can confirm that Reach outputs a PPS a signal timing which is compatible with the Livox unit.
Note that a PPS signal only delivers synchronization, not time. A clock ticks (or increments) every second and you can also read the time from it. A metronome ticks (or waves) every second, but it can’t tell you the current time. PPS is like like the metronome.
Your data must be recorded with a timestamp, so there must also be a clock that needs to be set. Anyway, if you find that you need a data stream with the current time, then Reach could do that too.