I have found that all three of my lo pro 7 trems have a different sweet spot. My UV likes to be tilted ever so slightly toward the rear of the guitar, just barely past parallel. The 2027 is dead parallel but the treble side needs to be up a touch. The 7620 I just got is also dead parallel but the bass side jacked up a touch. If I waver from these setting, it won't stay in tune.
Also, since your guitar is brand new, it will take some time for the springs to find "home" and the guitar will not stay in perfect tune until they do. In the meantime, double check your set up and then really abuse the trem, full on slack string dive bombs, bar flutters....really stretch those strings and do that every day for a while. Works like a charm and your guitar will feel less stiff.