@Hrrng327 Just to clarify, there are two separate issues here. The first is that you currently only have 4 GB free storage. That's not nearly enough for Windows to maneuver, let alone run a game like Sims 4, and it could certainly account for all the lag you're seeing. Please uninstall any programs you don't currently use, and move any files you don't need, including backup saves, to an external hard drive or flash drive. A good goal is 20 GB free, although a bit less is usually fine as long as you're not updating your operating system.
The other issue is that your hardware is not strong enough for TS4's more demanding packs. Neither your processor nor its integrated graphics chip is strong enough to handle the more recent expansions (e.g. Seasons, Island Living), and your computer might not be able to run them at all. Game packs and the early expansion packs are less demanding, although they do require more resources to run than the base game alone. Stuff packs only add minimal overhead.
Additionally, the cumulative effect of many packs will also stress your hardware more than just the base game. Even adding a few low-impact packs may make a significant difference in how the game runs. So if you're thinking of buying a few, please keep in mind that your computer is already likely close to the limit of what it can effectively handle.
The other consideration, if you want more packs, is that they'll take up some of that storage you're freeing up. Normally this isn't an issue, since even an EP will only take a couple of GB, but with the small margin you have, you'll need to watch your free storage carefully. The product page for each pack lists the amount of storage it will take once installed.
Edit to add: There are other issues you'll want to address regarding your graphics card. Its driver is out of date, which can be addressed easily enough. And it would help to allocate more memory to the card, although you'd need to be comfortable changing the setting in BIOS. You'd also see a benefit from installing more RAM, especially if you do allocate a larger share to the graphics card.
Once you've increased the amout of free storage, let me know if you're interested in making any other changes. At the very least, it's a good idea to update the graphics card driver.