Originally posted by: phisrow
I'd be a bit nervous about doing so. Now, it could be that the laptop interacts with its battery in some elegant, civilized fashion, e.g. feeds 12 volts(or some standard voltage) to charge circuitry built into the battery, in which case any such batter would do. However, that isn't too likely. If the charge circuitry is built into the laptop(particularly if it is the, shall we say, heavy handed charge circuitry that some older laptops are notorious for), a lithium ion battery could find its new home most inconvivial. In addition to being expensive, lithium batteries have been known to express displeasure with their users by catching fire. Not something to have in ones's lap.
My recommendation would be, if the battery life isn't good enough for you, to crack open the existing battery pack and examine the cells. If they aren't labelled as being one chemistry or another, trust what the battery label says. Replacement cells in both chemistries and all common sizes are easily and cheaply available online, from sites serving the RC and hobby robot enthusiasts. At this point it's pretty much a drop in job. A touch of soldering will be required(do get tabbed cells, if possible, to save yourself some hassle); but you'll be able to upgrade the tired old battery pack to modern, fresh, high-capacity cells of the appropriate chemistry for less than the cost of a second rate lithium ion pack.