Hello everyone how are you? I wanted to know if there are some departments that called LCPD?  

I'm sure there will be some small-town force, however I can't find any looking around Google

I've heard that there is something called "League City Police Department"

Well, there is a place called Liberty City (City of Liberty) in Gregg County, Texas: http://en.wikipedia.org/wiki/Liberty_City,_Texas

Their small police department is called "Liberty Police Department" though: http://www.cityofliberty.org/Departments/PoliceDepartment.aspx

 

rhode island has a Little Compton Police Department. 

Above was correct, there is a League City Police Department also in Texas. I live a few hours away, they are LCPD, though they don't use the abbreviation much that i've seen when passing through.