http://static.fraport.de/ONLINE/Flip...index.html#/6/
In short, yes. If it is on one ticket, LH will get you to your connecting flight or schedule you on the next one if you miss it. You clear passport control in FRA and then proceed to your Schengen gate. Follow the signs for connecting flights/anschlussflüge. An hour and a half is plenty of time.