Half of the screen turned white

Yep, that's a busted LCD, all right; the only fix here is to replace the screen. Luckily, iFixit already has a guide showing you how to take the broken one out and install a new one.

Lenovo X130e LCD Replacement - iFixit Repair Guide

The good news here is your laptop is one of the easy ones to repair; basically you just have to get the bezel off then there are only like four screws holding the LCD on. Remove those, then flip the screen down onto the keyboard and you can then unplug it. Reverse that procedure and you're done! Easy peasy. :)

With respect to locating a replacement part, I've used a couple of strategies. The first, and most obvious, is to search online using the full model number of your laptop. That will generally give you both new, used and aftermarket options; you'll have to determine if there are different screens being used; for example there may be a couple of different resolutions available and there may be a touch screen option that needs to be considered, so keep that in mind.

Another method I've used is based on the fact that very few laptop manufacturers build their own LCD's; they generally buy them off the shelf to match their system requirements. So if you open up the display and look on the rear side of the LCD, you'll find a manufacturer's sticker with their name and a model number of the actual LCD. Using that information to search will usually give you additional options for finding replacements. In some cases I've had luck with noting that while I was looking for a screen for an Acer Chromebook, it turned out that same LCD was also used on a Compaq laptop, so I was actually able to find someone selling a screen for the Compaq model number far cheaper than any other option I saw.

It all depends on how much work you want to put into a search vs. how much you're willing to pay for a replacement. I usually start out looking on places like Amazon, eBay and AliExpress, depending on my delivery time/quality/cost considerations. Amazon is usually fastest at delivery, but tends to cost a bit more. AliExpress is almost always the cheapest, but lead times from China can get long, while eBay generally falls somewhere in the middle.

Hopefully that'll get you going on fixing your laptop; as I mentioned, it's a pretty simple process and if you can use a screwdriver you can almost certainly do it yourself. Good luck and let us know how it all turns out for you!