Wow, talk about 1st world problems. 100 ping is top notch for me. Also, I recently discovered that the LAN server consistently gives me between 60-80 ping which from my perspective is unimaginably low. Hell, it's almost too good to be true. I've been playing since season 5 and I played the vast majority of that time with a 150 ping. Only relatively recently did I start getting 100 ping half the time on NA. I don't know the cause but whatever. I'm currently leveling an account on LAN so I could enjoy permanently having 60-80 ping one day.
Now, onto your topic about VPNs. For the past year, I've needed a VPN to play since someone must have blocked the client where I live. I've actually used several of them since and currently I use two VPNs to play. The problem is that most VPNs will raise your ping significantly. Luckily for me though, it is only the client that is blocked and not the game engine itself. So I only need the client to join games and I could switch off the VPN after the game has started if I want to play at my natural ping.
Now, I've been using these VPNs for free, which does impose certain restrictions. Most of them will only allow you access to a small subset of servers and they will limit how much data you can use. I'm assuming this is why my ping gets so much higher when I use them to play the game. I suspect that if I paid for them, I'd be able to choose more servers and ultimately choose a server close enough to me so that I get my natural ping through them.
However, there was one free VPN I found and the only one I found so far that gives me better ping than my natural ping. Playing without a VPN on NA gives me 150 ping some games and 100 some games. This VPN gives me 100 ping all the time. On rare occasions, it will go even lower, like 90. My natural internet would NEVER EVER give me 90 ping on NA. I highly recommend you check this one out. It's called WindScribe. Here's a link: https://windscribe.com/?affid=g2yha463
That might be the VPN you're looking for. As I said, it's the only one I've found that works better than my natural internet connection for League. There are a few servers available when using it for free. If you're playing on NA, use a server from US EAST. The Chicago and Miami servers work the best for me. Also, if you use it for free you get 10 GB per month. The average League match uses about 50 MB, so if you use it ONLY when in game, 10 GB per month is more than enough.