i have 8gb of ram and some games are lagging.
The question is why, though. Both your memory and your graphics card are potential bottlenecks. More memory might well help for gaming, but a graphics card upgrade would probably have a
much larger effect. Of course, you could do both. 2x4GB of DDR4-2400 is pretty cheap - £60 here.
£500 is a hefty budget, but there might be other issues. A 1050Ti has a very low power requirement - 75W. It's not uncommon for mid-high cards (which you could be looking at with your budget) to draw triple that. So you'd need to know if your PSU is up to that. Size is another potential issue - more powerful cards strongly tend to be physically bigger, sometimes much bigger. You'd need to know if it would fit in your case with everything else.
You may need to go into our BIOS and change the DRAM Profile to XMP - this should unlock and get you the 2400 MHz. I had to do with mine for 1600 MHz sticks. Worth a check!
It might also be a matter of where they're looking in CPU-Z. The SPD tab will show the highest JEDEC standard that the memory is compliant with...which tops out at 667MHz for DDR3. The memory tab will show the actual speed. Strictly speaking, anything above 667MHz is an overclock for DDR3 as it's not JEDEC compliant and that's why any memory rated higher it will be automatically set to 667MHz...and that's why I think your suggestion is more likely to be the correct explanation.
Also, as far as I know, its 2400 MHz of all the RAM Sticks combined, not individually but I could be wrong (unless you're running single channel?). For example my Dual Channels 1600 MHz sticks are running 800 MHz each.
It shouldn't be that. The potential for confusion stems from the fact that there are two ways of expressing the speed of DDR memory. The first is the cycles per second it's running at, the second is the number of transfers per second. DDR transfers twice per cycle, so a DDR stick running at 800MHz will (in a best case scenario) perform 1600M transfers per second and is therefore often referred to as having a speed of 1600MHz. Both are right, just in different ways.