Ok, I would presume that if all others connect well to the 600, the problem is with the Wireless adapter on the LT, drivers for the adapter or in the configuration.
What modes does the adapter on the LT support? single B , G or N mode? Did you try to connect G mode only, with no WiFi security? Does Single mode G with TPIK only work?
Ensure the drivers are up to date on the adapter.
Check with in the adapter configurations for any radio mode support and configurations there. Refer to the Mfr of drivers and configuration support.