I think it largely depends on your definition of "normal"

For me, "normal" has more to do with price stability, not so much price as such at whatever level. No doubt, if Bitcoin gets wider recognition as a convenient and reliable vehicle for wealth transfer, its price is set to rise, along with its real value. How real value is going to interact with speculative value in this environment is another question, though. For example, if more bitcoins get locked in payment channels (which is kinda expected with LN kicking off for real), less coins will get traded. But this will inevitably lead to higher volatility which is not a good thing for real use