LTM does not forward any IP packets for traffic it is not "responsible" for.
If you create a VIP on a port, LTM will forward traffic for this VIP/port to the backend servers. But any traffic from that backend servers to anywhere on the "other side" of LTM is not forwarded by default.
You need to create a "Traffic forwarder" virtual server which is of type "forwarding (IP)" and reacts to 0.0.0.0/0.0.0.0 as Destination Network on "* All Ports" and for "* All Protocols".
This virtual server has then be enabled on all vlans where you want the LTM to forward traffic.
As a last step, you need to route your VLAN 51 network to the VLAN 50 address of LTM and also put the VLAN51 address of LTM as default gateway on the nodes in VLAN51.