Sometimes nothing, but ...
"lies" specifies more than "is" does. With a person or animal, "lies" specifies a resting posture, such as a supine posture, as opposed to upright. With an object which can be regarded as having an upright orientation, such as a cup, "lies" would specify on its side or horizontal.
For a bonus, here's a link to the Duden's German definition of liegen: http://www.duden.de/rechtschreibung/liegen
Here is how I learned it: if it is about some movement (to put something onto the table) then it is accusative (auf den). But if it's just a state of some object that is currently on the table, then it is dative (auf dem). So it's mostly about movement. However, when you use "nach" or "zu", it's always dative, although it is indeed about movement. These two are exceptions that one needs to learn. For others it is all about movement
I found the reference below useful. (Spoken) English is definitely less specific. Perhaps spoken German is similar in practice? If a native German speaker could make a comment here (please), it would be appreciated. As an example, there is no concept in English regarding the position of the item which I have placed, standing upright is as good as laying on its side, it's on the table regardless. Some of the tools I have used while learning German make a distinction between the two concepts; example, a clock versus a watch. The clock stands on the table while the watch lays on the table. In spoken English, if I were to correct someone about the technicality of position on the table, some would politely ignore me while most would use more colorful language to express their opinion.