I was fan of TinyDO from start, only drawback is you cannot put date for reminder... so... I start searching for something with reminders and lockscreen support.
I found:
Hashnotes - excellent but broken after last update
Timekeeper - lots of bugs but I contacted developer and he seems to start working on update soon
Good Topic. People could also list tasks apps that sync, either with exchange/o365 or even outlook.com.
I have O365 subscription and been using Tasks by In The Hand. Which is pretty basic but gets the job done. There is also 2day tasks, but that's pretty heavy with all settings. Also I think Google sync is supported better than O365.