The basic principle is simple and it adheres to ANY system in the world..As there is more data to be indexed, the system becomes slower..This means, if you install more applications, and add more data, there will be more stuff to be searched by the system and render the memory accordingly..This, slows down the system..
For as long as the computer's capacity can calculate ALL the data in the computer per second, there will be no noticeable lag..This is how supercomputers function..They can perform millions of calculations in miliseconds and hence, maintain speed even with huge amount of data..
Android is no exceptional too..However, Android is fitted with smart memory management..When you are multitasking on Android, it manages the sets priority to the applications in the background and decides whether it will be needed soon or not..That is why, Android phones do NOT need a task manager or task killer..It has a built in one

So, the lag is not noticeable~ But if you're running a phone below 1GHz processor, you might experience lesser performance..If lag is a huge concern, choose between the top range Android phones..You will not regret

At least, its cheaper than the iPhone still