I just tested you code and every time PORTB.0 is connected to 0 volts(ground) the LED blinks and the LCD counts.

Here is what I have with a couple small changes. Look at comments.
Code:
DEFINE OSC 20

Define LCD_DREG PORTD
Define LCD_DBIT 4
Define LCD_RSREG PORTD
Define LCD_RSBIT 2
Define LCD_EREG PORTD
Define LCD_EBIT 3
DEFINE LCD_LINES 2 'Number lines on LCD

TRISB.0 = 1

led var PORTB.5 'CHANGED BECAUSE ICSP
counter var byte

OPTION_REG = %01111111 'Enable portb pullups and
'rising edge on B0 interrupt
On interrupt goto myint 'Define interrupt handler
INTCON = %10010000 'Enable INTE interrupt
counter = 0
'**** Main Loop ***
loop:
lcdout $fe,1 'CLEAR SCREEN
lcdout "Count=",# counter 'display count value
pause 50  'TIME TO DISPLAY
high led 'turn led on
goto loop 'Do it forever

'*****Interrupt Handler *****
Disable 'No interrupts pass this point
myint:
low led 'if we get here turn led off
Pause 300 'wait .3 seconds
counter = counter + 1
INTCON.1 = 0 'clear interrupt flag
resume 'return to main program
enable

end