Finally YOU made it!!!

I just changed my circuit to power it directly from my variable power-supply and simulate the batterie's weakening.

@5VDC, my display shows a value of 135 and @4,2VDC (can't go lower or my display won't work anymore) I read 147.

So, except the particular init sequence for the LCD I use, the code example here under is working fine and should be quite standard.

Code:
' PIC 16F690 Fuses
@ __config _FCMEN_OFF &_IESO_OFF &_CPD_OFF &_WDT_OFF &_HS_OSC &_BOR_OFF &_CP_OFF &_PWRTE_OFF &_MCLRE_OFF

'-------------------------------------------------------------------------------
' Registers   76543210
OPTION_REG = %10000000 'OPTION register
ANSEL      = %00000000 'Select analog inputs Channels 0 to 7
ANSELH     = %00000000 'Select analog inputs Channels 8 to 11
WPUA       = %00000000 'Select weak pull-ups
WPUB       = %00000000 'Select weak pull-ups
ADCON0     = %00000000 'AD Module
ADCON1     = %00000000 'AD control register
CM1CON0    = %00000000 'Comparator1 Module
CM2CON0    = %00000000 'Comparator2 Module
INTCON     = %00000000 'INTerrupts CONtrol
TRISA      = %00000000 'Select Input/Output (0 to 5)
PORTA      = %00000000 'Set High/Low (0 to 5)
TRISB      = %00000000 'Select Input/Output (4 to 7)
PORTB      = %00000000 'Set High/Low (4 to 7)
TRISC      = %00000000 'Select Input/Output (0 to 7)
PORTC      = %00000000 'Set High/Low (0 to 7)

'-------------------------------------------------------------------------------
' Defines
DEFINE OSC 8

DEFINE LCD_DREG PORTC  'LCD data port 
DEFINE LCD_DBIT 4      'LCD data starting PORT.bit (0 or 4)
DEFINE LCD_RSREG PORTC 'LCD register select port 
DEFINE LCD_RSBIT 3     'LCD register select bit 
DEFINE LCD_EREG PORTC  'LCD enable port 
DEFINE LCD_EBIT 2      'LCD enable bit 
DEFINE LCD_BITS 4      'LCD bus size 4 or 8

DEFINE ADC_BITS 10     'Number of bits in ADCIN result

'-------------------------------------------------------------------------------
' Init display

' ELECTRONIC ASSEMBLY DOGM081 LCD display Mandatory settings
'  See datasheet for circuitry changes by 5V or 3,3V operation
PAUSE 1000      'Time to settle Vdd (THIS IS CRUCIAL FOR THIS DISPLAY!!!)
LCDOUT $FE, $29 'Function Set: 4 bits bus mode
LCDOUT $FE, $1C 'Bias set
LCDOUT $FE, $52 'Power control + Contrast (HiByte)(for 5V=$52 or 3,3V=55)
LCDOUT $FE, $69 'Follower control (5V=$69/3,3V=6D)
LCDOUT $FE, $78 'Contrast (LowByte)

'-------------------------------------------------------------------------------
' Variables
Bat_Value   var word 'holds ADC value
Bat_Value   = 0

'-------------------------------------------------------------------------------
' Start program

MAIN:
    ADCON0=%10110101   ' Here we drive the 0,6 volts to the ADC
    'ADCON1=%00110000   ' I prefer to be sure to have FRC for the beginning at least
    VRCON= %00010000   ' Enable the VP6 reference
    ADCON0.1=1
    WHILE ADCON0.1 : WEND
    Bat_Value.HIGHBYTE = ADRESH : Bat_Value.LOWBYTE = ADRESL
    LCDOUT $FE,2,DEC4 Bat_Value
    PAUSE 1000
GOTO MAIN

END
Using the internal 0,6V reference:
- 0,8Vbatt difference = 12 value change
+ no external components

Using an external voltage divider:
+ 0,8Vbatt difference = 84 value change
- external components


Thanks a lot for all your help