Is there a LCD which can display analog signals without converting to digital signals?

 

No...there isn't!

 

If you don't mind the size (and the price ), look up panel meters. These are small boxes with LED or LCD displays complete with the circuits to accept different input signals, usually for industrial monitoring.

There are meters for all sorts of signals, such as freq, counter, voltage, etc.

There's also a cheaper one, with 3,5 digit LCD and ICL7106 IC (IIRC) that can display voltage directly, sadly I don't remember the part # or type anymore.

Edit:

Have a look at this page.