You don't mention distances between the 2 networks so I am assuming they are not too far apart and the 2 networks are physically separate (not 1 network with 2 gateways) so for that scenario you will need a router to bridge the two.
One solution, depending on distance and locations would be to connect the NAS to an INSIDE port of an added router and connect one INSIDE port to the LAN1 router. Disable DHCP on the added router and give the router and NAS a static IP on the IP range of LAN1.
This would mean the that users of LAN1 can go to
\\host.of.the.NAS\\share and access that share.
Next, connect the OUTSIDE port of the added router to the inside of LAN2, unless you set a static IP the OUTSIDE port should automatically get an IP from the DHCP server in LAN2. Put the INSIDE IP of the NAS on LAN1 in the DMZ of the added router (or configure port forwarding as required), users can then go to
\\ip.of.outside.portonrouter\\share to access it. The router will then forward from the LAN2 IP to the INSIDE LAN1 IP of the NAS.
A user on LAN1 will not be able to connect to LAN2 and users of LAN2 can only connect to any routing you've enabled on the added router.
Another, and depending on your routers would be to set up site to site vpn but this is slow and awkward.