I know that the Roman Catholic Church has the same Gospel reading on the Lord's Day. But does it having a daily reading as well? Where can I go to find it?
Yes they are called Mass Readings, you can can see what is available on most Parish or Diocesan websites.
Here is a link to the US Bishops site, giving the readings for today (it will update each day)... https://bible.usccb.org/daily-bible-reading