switch – Connect 1 device to 2 different networks

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I have 1 device that needs to connect to the internet trough a router with DHCP, and to a LAN that is used for a local system (this is in a hospital). This device is windows based and unfortunately, only has 1 network card and it’s impossible to add another one (it’s a medical device). Both the router and the LAN have different IP segments (router is 192.168.1.x and LAN is 10.90.1.x), and I need my device to be able to connect to the internet trough the router, and also access the systems on the LAN, but there should not be any traffic between the router and the LAN . It would look something like this:

An issues here is that I cannot change pretty much anything either on the router side or the LAN side since, as stated, these both belong to a hospital.
I am assuming a managed switch (with L3 capabilities), configuring VLANs with a trunk port, and routing traffic on said switch are needed for this, but I’m not so sure since my networking knowledge is not that deep and I have never done this before.
Am I assuming correctly, could this be solved with a managed switch? If so, how should I configure my managed switch? Should I put router port and device port in VLAN1, and LAN port and device port on VLAN2, and make device port a trunk port? which switch should I get? maybe a Cisco Business 250 would do? Otherwise, how can I solve this? Is it possible to use an L2 switch and a router?