By default, every NTP client sends maximum one request per 64 seconds, so 10,000 requests per second could serve at least 64*10,000 = 640,000 clients.

Current implementations of NTP increase the polling interval from 64 seconds up to 1024 seconds after time synchronization is stable. Assuming all clients would follow that rule, a LANTIME capable of handling 10,000 requests per second could serve 1,024*10,000 = 10,240,000 clients.

Anyway, if you need to synchronize such a large network, you should not let all client stations contact one LANTIME directly. Instead, it is recommended to set up a hierarchical time synchronisation tree, e.g. servers in the different departments/network segments synchronize to the LANTIME, and the workstations in each department synchronize to their nearest server(s).