WISP Client Router offer you this show I was very useful and I wanted to get it

You can try to find this router,TL-MR3020.
It support 3G/4G,WISP and AP mode.

Do you know if it is true WISP or just infrastructure client?

I have been looking at it but haven't procured it yet. My experience thus far is that a LevelOne WISP AP that is supposed to be a routing WISP client, doesn't do that thing at all.

Does it allow me to set up my own LAN that is routed to the internet?

Regards, X.

Do you mean you want to connect to a front wireless network and share the network for other clients?
If so,MR3020 can do the job.You can check the settings here.
http://www.tp-link.com/resources/simulator/TL-MR3040N/3040_wisp_client_router/Index.htm

Yes but the shared network must be its own network/SSID.

This LevelOne device seems to support it, but it doesn't work.

The MR3020 interface (web config) seems rather simple, but that is plenty. I think the "big switch" is that hardware knob that selects the mode.

Easier than LevelOne certainly.