If I connect the LCD all of my serial echo is lost and on the LCD the first two caraters show a fast flashing cursor.

If you condense to

run	jnb	RI,	$	; Wait for the 8051 to set the RI flag
	mov	A,	SBUF	; Read the character from the serial port
	clr	RI		; set for next character
SEND	clr	TI		; Be sure the bit is initially clear
	mov	SBUF,	A	; send character
	jnb	TI,	$	; Pause until the TI bit is set. 
	acall	WRITE_LCD
	sjmp run

you will see that you need the time to transmit a character AND the time to write it to the LCD before you come back to examine thr read character buffer. If your PC (or whatever) write at full speed (no gap between characters) you will get buffer overrun.

Convert the whole shebang to interrupt driven and come back.

Erik