That's perfectly normal then.
The OEM double tap to wake system is in Microsoft Lumias too and even in many other phones these days, even in Huawei.
Factory fitted double tap to wake system is linked with proximity sensor, so when the proximity sensor is covered (e.g phone is in pocket, flip cover closed etc), the touch digitizer turns off to save accidental touches and waking up.
When the proximity sensor is uncovered (flip cover opened, phone out of pocket etc), touch digitizer becomes active to register double taps.
Do you have exactly the same system?.
I prefer the other way, i.e the screen turns on automatically when it detects a change in proximity sensor state, i.e waving hand over proximity sensor or taking phone out of pocket automatically turns on the screen, without touching the screen. That's much better, convenient and battery friendly than double tap to wake, IMHO.
I use this app sometimes and this setting. Though not a fan of this.
Take a look at "Auto Screen On Off(Smart Cover"
https://play.google.com/store/apps/details?id=com.danielkao.autoscreenonoff
