Is there a wifi (LAN) speed tester?

The short answer is no — LAN speed cannot be tested using just a phone by itself; it needs a proper testing setup to be measured correctly, which most users won't bother to do, so it's questionable whether it's worth my time to implement a feature most people won't use.

Long answer:

To perform a speed test, there must be some device from which you perform the download and to which you perform the upload. The download/upload test files have to be downloaded/uploaded from/to some other "server" device on your LAN, and the speed of that transfer will be measured. This requires some setup, and ordinary smartphone users want something where you just tap a button and it works.

The next problem is that the test will be limited by the slowest device in your test setup — it could be limited by the computer acting as the server, by the wifi technology used by your router or your phone, by the CPU speed of your phone, etc. The server device should be connected to the router by wire; otherwise both the sending and receiving devices use the same wifi network, which affects the resulting speed considerably (the result won't be just half of the maximum speed but much less — there will be collisions that will slow down the speed a lot).

If you are willing to invest some time to properly set up your network for the test and know what you are doing, you can get a testing server called iPerf (a kind of standard for LAN speed testing) here

https://sourceforge.net/projects/iperf2/

and use an iPerf app from the App Store (search for the word "iPerf"; there are several of them — I haven't tried them, so I have no personal recommendation).