We have a lease line between two sites. When the line is down and I ping to the router on the other site, we normally get the answer "Request timed out," but now we get the answer "TTL expired in transit." What does it mean?
The "Request timed out" error occurs when the computer you're pinging from doesn't ever get a response back. So, it would be symptomatic of a leased line that is simply down and can't reach the Internet. The "TTL expired in transit" error will only show up if a router that is forwarding the traffic sends an error message back to the computer you're pinging from.
TTL (Time To Live) is a number that is used to track the number of hops or routers a particular packet crosses. If a packet crosses too many routers, an error is returned to the computer that sent the packet. This is to prevent routing loops where a packet is forwarded between two or more routers indefinitely. In short, it means you have a Layer 3 network problem instead of a Layer 1 network problem, and you should call whoever is responsible for your network infrastructure.
More on TTL when pinging
Troubleshooting Windows network connectivity with the ping command