|Is there a way to connect the two LAN's without using an internet connection? Thanks|
There's only two possibilities I can think of and both are a whole lot more expensive than getting an internet connection for network 2 and setting up a VPN between them.
1) Dedicated fibre optic connection between locations
2) Enterprise level Point-to-Point wireless shot between locations.
I suggest you get internet at your second location if at all possible.