AFAIK, all *.bosh-lite.com resolves to 10.244.0.34

Did you setup via vagrant or manually? There scripts within the VM itself that will add iptables rules to route traffic to proper interface for 10.244.0.x if I remember correctly. My bosh-lite.com setup is a bit different due to some reasons that I can't use vagrant on my machine but I would suggest vagrant for simplicity.

I don't remember what's the subnet created by vagrant for the VM, but you might need to use 10.244.0.34 if it's not using the 192.168.x.x network.

Also, make sure you are able to ping the containers in bosh-lite. In the VM itself, perform a 'bosh vms' to check all status of warden containers, if some not responding use 'bosh cck' to repair them (usually happens after your VM restart).