It would be quite rare for a web server to be dedicated to the WinLIMS.NET application. The processor used by the Web Server is highly dependent on the number of other applications that are using the same database server as well as the number of concurrent users who are accessing the database. Note that the same server can be used to run both the WinLIMS.NET software and the underlying database engine.
Should the database server be dedicated to the WinLIMS.NET application, a Dual Pentium (or better) will be more than adequate for a typical 20 concurrent user system.
It is always best to follow the general rule; "You can never have too much computing power." and with the lowering cost of hardware, it is far less expensive to add 'horsepower' to your system to maintain good performance than it is to ever have system slowdown due to a few dollar's worth of processing power.