Will having the car serviced at a non LR Dealer for the 3rd service (therefore out of warranty) affect the resale value or should I keep the "Full LR service history"

I thinks it's generally accepted that having only a partial LRSH will affect resale value. However I very much doubt that the drop in value would equal the amount you would have spent on LR servicing. I'd go for independent specialist....  Current: I can't say...Oh the Shame!
Gone: 2003 Audi S4 - 340BHP of Fun
Gone: 2005 RRS SE, Silver, Chrome Mirrors, Tinted with a stupid spare wheel!
Gone: Audi A4 2.5 TDi Quattro 180bhp
Gone: BMW 535i
Gone: 1985 Audi Quattro
Gone: Subaru Imprezza Turbo (rubbish)