1.) For years I have used Hoppe's 9 cleaner and Hoppe's Oil with very good results.
2.) For the past x2 years I been using Break Free CLP and have had been very happy. Others here may have more suggestions.
*I also keep Rem Oil around for light uses.
3.) Threads on cleaning are fun to read because of the many different ways and products. Read the manual and try what you can. It does depend on the firearm and keeping a firearm clean is important. I love the process of caring for these firearms it is therapy for me.
4.) Keep looking for videos on what to lube and where. Some members may chime in here and assist on your LCP. Look at the manual or download it from Ruger.