I've modified the code according to the answers.

But with or without the 32,768kHz crystal, the LED will always blink.

As per datasheet, I have enabled LP oscillator. Why should I set the internal oscillator instead please?

Same question for T1CON.TMR1CS; why should I set this one?

Code:
' ====== FUSES ====================================================================================
' PIC 16F690
 __config  _INTRC_OSC_NOCLKOUT & _WDT_ON & _PWRTE_OFF & _MCLRE_OFF & _CP_OFF & _CPD_OFF & _BOD_ON & _IESO_ON & _FCMEN_ON

' ====== INTERRUPT SERVICE ROUTINE ================================================================
GOTO INIT: ' Just to place ISR at top of program
DISABLE
ISR: 'if TMR1IF is set (TMR1 has overflown)
    toggle PORTB.6 'LED
    PIR1.0 = 0 ' clear TMR1IF overflow flag
    resume
ENABLE

' ====== INITIALIZE ===============================================================================
INIT:
PAUSE 1000 'circuit settle time

' ====== DEFINES ==================================================================================
DEFINE OSC 4

' ====== REGISTERS ================================================================================
'             76543210
OPTION_REG = %10000000 ' Pull-Ups disabled
OSCCON     = %01100000 ' Internal RC set to 4Mhz
ANSEL      = %00000000 ' Analog inputs Channels 0 to 7
ANSELH     = %00000000 ' Analog inputs Channels 8 to 11
INTCON     = %11000000 ' INTerrupts CONtrol: GIE is ON, PEIE is ON 
T1CON      = %00111011 ' Timer1 OSC enabled, Timer1 enabled, presc.1:8
PIE1       = %00000001 ' Enable TMR1IF overflow flag

' ====== PROGRAM ==================================================================================
ON INTERRUPT GOTO ISR

MAIN:
    goto MAIN:
END