You are having problem with overlapping IP addresses on Lan. This is possible and you can configure it.
I am assumsing that you have 192.168.11.0 subnet on both sides Lan network.
For VPN you have to make a different configuration.
in VPN you will NAT one side of VPN interesting traffic into different subnet which will be global.
and remote Lan will access this IP via VPN tunnel and then it will translate into private IP address of LAN 2.
I am running this step, where my remote network is having the same IP scheme that I am using on my lan, i did this on VPN concentrator but this is possible on firewal/ASA as well.
Please see the below mention link.
http://www.cisco.com/en/US/products/hw/vpndevc/ps2030/products_configuration_example09186a00808c9950.shtml
If you still have the problem please let me know