Is there an app available from the App Store (iOS) to find out the LAN speed?
If you want to measure the speed (bandwidth) between your iPad and your PC, take a look at iperf.  It is available for computers and there are versions on the App Store for iOS too (the one I use seems to have gone away, but searching the App Store for "iperf" reveals several possible options).

You run an iperf server at one end (eg the PC), and a client at the other (eg the iPad).  It runs for a configurable amount of time (I think the default is 1 minute), and then tells you how much data it managed to transfer.

Compared to eg copying a file, the figures you get this way are a more accurate reflection of the available network speed, because copying a file requires retrieving the data from a hard drive, writing it at the other end, sending acknowledgements, the overhead of the file transfer protocol etc... iPerf is simpler than that: it just transfers data as fast as it can.