Thankyou for replying again.
Here is what I have done so far...
' Used Microcontroller:
INCLUDE 89C4051.mc

' Used Portpins:
Button1 EQU P3.0
Button2 EQU P3.1
EN EQU P3.2 'ENABLE
RS EQU P3.3 'REG SELECT
RW EQU P3.4 'READ/WRITE SELECT
'DB7 EQU P1.7
DATA EQU P1
' Used RAM Bits
Direction BIT 0h
STOP BIT 0h

Start:
MOV DATA,#FFh 'Init: Set all pins from port 1 to high
MOV PORT3,#00h 'Init: Set all pins from port 3 to high

'Initialise the LCD
CLR RS
CLR RW
LCALL short_wait
SETB EN
LCALL short_wait
MOV DATA,#30h
NOP
NOP
CLR EN
LCALL short_wait
LCALL short_wait

CLR RS
CLR RW
LCALL short_wait
SETB EN
LCALL short_wait
MOV DATA,#30h
NOP
NOP
CLR EN
LCALL short_wait
LCALL short_wait

CLR RS
CLR RW
LCALL short_wait
SETB EN
LCALL short_wait
MOV DATA,#30h
NOP
NOP
CLR EN
LCALL short_wait
LCALL short_wait

CLR RS
CLR RW
LCALL short_wait
SETB EN
LCALL short_wait
MOV DATA,#38h
NOP
NOP
CLR EN
LCALL WAIT_LCD

CLR RS
CLR RW
SETB EN
LCALL short_wait
MOV DATA,#0Eh
NOP
NOP
CLR EN
LCALL WAIT_LCD

CLR RS
CLR RW
SETB EN
LCALL short_wait
MOV DATA,#06h
NOP
NOP
CLR EN
LCALL WAIT_LCD

LCALL CLEAR_LCD

MOV A,#FEh 'Set accu to FE(hex) = 254(dec) = 11111110(bin)
Running_Light:

JB Direction,Check_1 'Jump to "Check_1", if bit "Direction" is set
INC A ' Else Inc Acc
Check_1:
JNB Direction,Check_2 'Jump to "Check_2", if bit "Direction" isn´t set
DEC A 'Else Dec Acc
Check_2:
LCALL Wait 'Jump to wait
LJMP Running_Light
Wait:
MOV R0,#7Fh 'Set register R0 to 7F(hex) = 255(dec)

Wait_2:
JNB Button1,Wait_3 'Jump to "Wait_3", if button 1 not pressed
SETB Direction 'Set the bit "Direction"

LCALL search_table 'Search & O/P Data

Wait_3:
JNB Button2,Wait_4 'Jump to "Wait_4", if button 2 not pressed
CLR Direction 'Clear the bit "Direction"

LCALL search_table 'Search & O/P Data

Wait_4:
MOV R1,#7Fh 'Set register R1 to FF(hex) = 255(dec)

Wait_5:
DJNZ R1,Wait_5 'R1 = R1-1: Jump to "Wait_5", if R1 > 0
MOV R3,#FFh 'Set Register R3 to #FFh
MOV R4,#09h 'Set Register R4 to #09h
LCALL Wait_6
DJNZ R0,Wait_2 'R1 = R1-1: Jump back to "wait_2", if R0 > 0

RET 'Jump back to "Running Lights"

Wait_6:
DJNZ R3,Wait_6 'Long Wait Loop
DJNZ R4,Wait_6 'Long Wait Loop
RET

CLEAR_LCD: 'Clear the display
CLR RS
SETB EN
LCALL short_wait
MOV DATA,#01h
LCALL short_wait
LCALL short_wait
CLR EN
LCALL WAIT_LCD
RET

WAIT_LCD: 'Wait for LCD to become free
CLR RS
SETB RW
LCALL short_wait
SETB EN
LCALL short_wait
WAIT_LCD2:
MOV DATA,#FFh
MOV B,DATA
JB B.7,WAIT_LCD2 'Wait for bit 7 tu drop
CLR EN 'Finish the command
CLR RW
RET

WRITE_TEXT:
SETB RS
CLR RW
LCALL short_wait
SETB EN
LCALL short_wait
MOV DATA,A
LCALL short_wait
CLR EN
NOP
LCALL WAIT_LCD
RET

search_table:
'PUSH ACC
MOV R7,A
MOV DPTR,#0000h
MOV DPTR,#table 'point DPTR @ table

loop:
MOVC A,@A+DPTR 'get a character
JZ exit 'jump if acc 0 to exit
LCALL WRITE_TEXT 'write it to the port
INC DPTR 'get next char
CLR A 'clear acc for next character
SJMP loop 'loop back to get a character

'exit of acc = 00


exit:
'POP ACC 'pop back the value of the acc
MOV A,R7

RET

short_wait:
MOV R5,#FFh
MOV R6,#0Fh
short_wait2:
DJNZ R5,short_wait2
short_wait3:
DJNZ R6,short_wait3
RET


table:
DB "TX1240.0",Stop 'Just an experiment seems to work
DB "TX1240.5",0h
DB "TX1241.0",0h
DB "TX1241.5",0h
DB "TX1242.0",0h
DB "TX1242.5",0h
DB "TX1243.0",0h
This goes on for DB "TX1367,5"