I bought my brand new phone with the Android Version of Lollipop 5.1 out of the box, does that mean Lollipop 5.1 is the phone's stock ROM?
Stock Rom is basically the software which is provided by the vendor or You may can say that the software which was installed by the manufacturer of the phone is Stock Rom. the other type of the Rom is Custom Rom which advance users installed after flashing it as per they desire.
And Yup in your scenario you have Stock Rom of "Lollipop 5.1". You may install any custom Rom as per your own risk. if you know well how to flash custom Rom.