"...so how will the receiving device (PC in my case) know whether if the data on TxD and RxD is due to Serial Transmission or other reason?"

You have connected two devices (LCD and PC COM) to
your TxD and RxD pins of 8051. Is it true?
What is the reason of such solution?

"Your pulse stream is framing into a sequence that approximates (to the 8051 Uart anyway) a serial word. Change the sequence and you may not frame."

Maybe, but a SIO receiving is initiated if the start bit is evaluated.
The start bit evaluation instant depends on the concrete SIO device.
PC ACE (16C550,...) sample clock is situated approx. in the middle of the start bit,
I think, but in this case is better to read up documentation and data sheets.

Vaclav