I am doing a project, in which I need arduino always on I do not require much power, it is only two sensors and an LCD, my question is how long can I have arduino working without pause, one day, two days, one week?
If you have power, an Arduino can run for months with no problem.
I have a couple that have been running 24/7 for over a year.
I've had a 3.3 volt Arduino Pro Mini in my pump house controlling a 300 watt heater with a SSR and sending temperature and heater status via nRF905 radio for 2+ years with nary a hitch.
Basically, it will run forever unless your code or libraries are buggy. I had one that ran for five years or so that was only restarted by the occasional power outage or if I noticed it had died. The source of crashes was the wifi library I was using but even so it would go months without issue once the more egregious of the bugs in it were gone.
And you can use the Watchdog Timer to recover from crashes without human intervention. But it is much better to write bug-free code