How to drive four displays from DELL Precision 5520 with Dell Dock WD15 and native ports??

It's not going to be possible without some other type of hardware purchase - no.  The internal GPU cannot drive four displays at a time.

"some other type of hardware purchase" - What will that some other type of hardware be?

One or more USB to HDMI/DVI/VGA adapters, or something like the D6000 dock will let you drive 3 displays just off that dock. Either of those use DisplayLink chips to drive external displays rather than driving them directly by the GPU, so you can run up to 10 DisplayLink displays on top of whatever you run directly off the GPU. However, DisplayLink has its share of drawbacks that I’ve posted about a few times here.

Ok, now that I'm in front of a real computer, I'll give you a longer answer.  First, for the USB adapters I'm referring to, make sure they use USB-A ("regular USB") connectors, not USB-C, because display dongles that use USB-C will almost certainly be tapping into the GPU output that's wired to USB-C ports, and therefore those displays would count toward the max 3 displays that can be driven by the 5520's GPU.  The D6000 dock is a notable exception to this general guidance.  Second, make sure you check the maximum resolution supported on these adapters.  Some can go as high as 4K, but that is not always the case.

Ok, so here's how DisplayLink works.  Instead of having the GPU drive a DisplayLink display directly, a driver is added to the system that causes the CPU and GPU to render that display's image internally, then compress that image and send it over USB as regular data.  The DisplayLink chip inside the adapter then decompresses it and sends it to the display.  This compression behavior means that even on a fast system using USB 3.0, under certain conditions you may observe compression artifacts (e.g. blockiness) or sluggish motion.  One problem condition is when large portions of the display are changing simultaneously, e.g. watching full-screen video or gaming, since that means a lot more data has to be compressed and transmitted than when you're just typing an email and 98% of the display is static.  When I've watched full-screen video on a DisplayLink display, the video sort of alternates between slow motion and fast-forward, so on average it stays in sync with the audio, but it looks awkward.  Other problematic scenarios are when your CPU is bogged down on some other intensive task, leaving less performance available to perform this display data compression, or if your USB bus is saturated with some other traffic, such as transferring a lot of data to/from a fast drive, leaving less bandwidth to get the display data to the display.

On the other hand, for a display that's being used for regular office productivity tasks, DisplayLink is usually just fine -- and of course, it's also your only option for exceeding 3 displays anyway.

In addition to all of the above, why are you connecting a display directly to the laptop's HDMI output?  Wouldn't it be more convenient for you to have that connected to the WD15?  Or is one of your displays higher resolution than 1080p?  The WD15 can only do dual displays up to 1080p due to bandwidth limitations of USB-C when it's also being used to carry USB traffic (to handle the dock's USB ports).  The TB16 dock, which the 5520 also supports, can handle dual displays up to 4K and even some triple-display configurations, since it has 4x the display bandwidth of the WD15 available, but you're still limited to 3 GPU-driven displays total.