Mysql4.1 as a backed language
If by backend language you mean server side scripting, then that's wrong. MySQL is not a server side scripting engine. It is a database engine. You can connect to it and query it remotely, but the coding would be on your client side application. You could use a server side application to query and pass data back and forth to your client application. But your current description of MySQL is incorrect.
so is it possible to access this application within LAN connected PC
Yes, this is possible. You just need to connect to it using th IP address or server name of the remote computer.
do i need to install .net framework on LAN connected PC's(or on client PC's)
They're all LAN connected PC's so I have no idea what you're referring to there. You would install the .Net framework on the client PC's, but they most likely have it installed already. You would install it on the server PC as well if you plan on writing a backend application as an additional interface to the database engine.