This is a little more complicated than the question appears on its surface. Essentially, which charge states are possible when a particular atom of an element gets ionized depends primarily on the electron structure. That is the essence of chemistry, really. You need to understand how electrons occupy the space around the nucleus to understand which conditions are most energetically favorable. Those most-favorable conditions are where the atoms will end up if given the opportunity. Sometimes this is achieved by "stealing" electrons to fill up a level, and sometimes it is achieved by giving up electrons to empty a partially-filled level.
Now, if you have a compound and you want to know how to define the charge on each element in that compound, there are a set of rules to follow. I am not going to repeat them here, but the essential idea is that you assign the negative charges first, and what is left has to be the positive charge that makes the molecule be neutral (unless of course we are talking about some sort of ion complex, in which case you have to total to that charge on the ion complex).
In other words, you are asking about the basics of chemistry, and that is not something that can be explained adequately in a short few paragraphs. If it were so simple to explain, there would not be much point in having an entire year of schooling to teach it.
Lithium will almost always have a +1 charge when found in a compound. It cannot ever have more than a +3 charge because it only has three protons and three electrons. It could, conceivably, have some sort of negative charge, but that is extremely unlikely. The nucleus is too weak to hold onto more electrons; you would have to combine Li with something else that has an even weaker hold on electrons, and there really isn't much that does.