You shouldn't need to turn the timer off. And doing so will affect the accuracy of the Elapsed Timer.
And the Interrupts won't interfere with the MSSP module.

I think you just need to wait for the SecondsChanged flag before sending it to the LCD.
Then it won't be changing the time while you're trying to display it.

Code:
HauptSchleife:
    IF SecondsChanged THEN
        SecondsChanged = 0
        GOSUB EBSLCDZeile1
        ARRAYWRITE LCDText,[DEC2 days, "+", DEC2 Hours, ":", DEC2 Minutes, ":", DEC2 seconds, REP 32\11]
        GOSUB EBSLCDTEXTOUT
    ENDIF
    PAUSE 1
GOTO HauptSchleife