Which model, the first or new Second Generation? They are two different guns.
In terms of choosing a "pocket" pistol the newer version isn't as small or light. The older version is also hampered with a trigger that is less than stellar, and it has a lot of perceived recoil compared to other guns nearly identical in size and weight. The lack of a last round hold open doesn't sound like a significant issue until you try practicing with it, at which point you find yourself pulling the trigger on an empty chamber.
That can and will happen when you don't need it to in self defense. It's the specific reason Ruger now includes it in my opinion. Too many of us criticized it for that lack. It also make shooting at the range less fun, too.
It's like buying cars, you are better off test driving the short list to see what you expect and what they deliver are actually in the same ballpark. If at all possible get thee to a rental range and actually shoot some guns to see what you might like.
First, tho, put together a list of the features you actually need in that gun to see which actually qualify for consideration. The LCP lacks in some areas where others shine, and it the gun is less comfortable shooting and you therefore practice less with it, then that has a significant influence on whether you should trust it in carry. When I went down the list of features I needed, and came up with a short list, they all had last shot hold opens, had a measured trigger pull under 7 pounds, and that trigger was not overly long. That is what eliminated the RM380 for me, and why I found myself pleasantly surprised to discover the Kahr CW380 at the top of the list.
Just because it's cheap and popular doesn't mean it qualifies for your use. Shooting it should have a say so that you make an informed decision. I sold my first Gen LCP and plenty of others are for sale on Gunbroker, there's a reason for that. There are better guns for the money and even Ruger has abandoned the concept by moving into a larger replacement.