Why where travelers being warned that if they rode on lusitania they would have to do so at their own risk

Due to the german subs that patrol the water it was a very high risk of it being destroyed thinking it was delivering supplies

Because at that time, The pathway to Lusittiana was a territory conquered by the Germans troop during their conflict with Great Britain in World War I. The Germans give the warning following the international law of warfare at that time that indicates each nations should give warning to normal civilians if they intended to target a certain area.