Many Sprint/VZW LTE sites are getting 50-70ms even with some load. But yeah, 100ms+ for a new site is not all that great. Maybe it's just a matter of tuning.
I'd be interested in seeing a traceroute done from the LTE network. If it's anything like my HSPA+ AT&T connection, before you even get out onto the Internet you have to go through 12 AT&T router hops.
The LTE network's latency is barely lower than the HSPA+ network (which usually rides at 120-200ms).
I just did Sprint LTE traceroute in Android app, with about 60ms latency.
As expected, the link from cellphone to tower has most of the latency, not between cellsite and destination. If the cellsite is also using microwave or something wireless, it may then add more latency. It took 10 hops to get to Google but most of the bottleneck in latency is mostly phone to cellsite.
reply to XANAVirus I'll go out on a limb and state that LTE and HPSA+ are riding the same backhaul for most of AT&T, which in that case, may be not enough.