What's the difference between ram and memory management?
RAM is Random Access Memory. ROM is Read Only Memory (which can be written to - it's actually EAROM - Electrically Alterable Read Only Memory). You can't really "manage" ROM. That's where your apps and data are stored, and about the only "management" you can do is uninstall apps.
RAM management is removing references to apps that are in RAM but aren't currently running. It doesn't save more than nanosecconds -
if Android doesn't need that app to be in RAM and be called on regularly. If it does, you remove the app (you're actually removing the reference to it, so th space it's in is considered unused), Android reloads it, your "mamagement app" removes it, Android reloads it, etc., slowing the phone down and killing the battery.
The lag generally or at least is most noticeable when Web browsing.
When you "connect" to a web page (you don't really - the web is a disconnected model), you get the page, then anything further on that page happens in the browser.
If the "lag" happens when you do things on that page (tap something to enter information and it takes a second or two for the text box to come up) that's a slow Javascript interpreter in the browser. (Internet Explorer 5.5 was notorious for that - what took 20 seconds in Firefox wasn't near completion in 30 minutes in IE, and I killed it.) Use a different browser.
Atlas Web Browser is about the fastest one I've found. Not much fancy stuff, but fast when you want speed.
If the lag happens in opening a new page (clicking a link), that could be the internet. A web page should load in 1 second or less - that's what it says in the book. The book was written in the early 90s, when a flashing arrow was considered the ultimate in animation. These days, there are pages that take 10 seconds to load over a good connection on a fast browser. Blame everyone's desire to monetize websites and put up sites with 50% graphic advertising or more, tons of Javascript that really add very little to the user experience, and people who just don't know how to write websites. (Looking at the source of a page, I still see new sites that have code that was brand new - in 1998. Tons of stuff that could be done in a few lines of CSS. It tales a long time for the browser to read all that stuff and figure out hat to do with it, and there's no need for it. [And I'm not talking about this site - we have a bug here - and I'm glad I'm not on the team that has to find it. It's one of those, "now you see it, now you don't" things, and that's why the life expectancy of a web developer is less than that of a sky diver who doesn't use a parachute. Almost no one is affected by it, but it's annoying when it happens. But the site is written well.])