The only way to find out if the Lightning Network is working, is to try it out. Some people complain about unsuccessful payments while others are excited about how fast and cheap they are. If you don't want to bother with syncing up a full node then use one of the mobile wallets which you have posted.
There are quite a lot of shops which accept Lightning Network payments so you can easily test it by yourself.
Take a look at
this topic in which I tried to answer the most common questions regarding the Lightning Network.