Can an IC switch on another IC?
or can an IC can give enough voltage supply to be supplied to the Vcc of another IC?

 

Yes for some combinations of ICs and power supplies.

Ask a more detailed question an you will receive a more specific answer, if you like.

 

Possible, but this would be poor design.
It is better to use an ENABLE function or the equivalent of an AND gate.

 

It is used by my C code for LCD (Hitachi character LCD).

Otherwise the correct functioning is not guaranteed.
They easily freak from poor or noisy supplies they are slowly rising.
To a degree the displays are totally unrelieable for startup.

Solution 1: Invest in complicated regulation.
Solution 2: Switch ON the LCD after power has stabilized.

Microcontrollers have a power up timer which in the early 1980s was not known.

For >10mA, not normally. One would use a PNP BJT or a digital MOSFET.

 

Can an IC switch on another IC?
or can an IC can give enough voltage supply to be supplied to the Vcc of another IC?

Well... it's a definite maybe completely dependent on what these two IC's are.

I've done it in a few isolated cases where the driven IC did not need much current (say 5 mA max) but usually a transistor or fet is needed to handle the current without a large voltage drop.

Works better with CMOS outputs the TTL.