This is frequently due to an inability to establish or maintain a connection to the iTunes Store. The following article provides some useful information and troubleshooting steps that can help restore this connection.
I read that the problem might be that your iTunes account "thinks" it has 1 item to download and keeps trying to access it until it kind of times out and brings up the "connection lost" message. My iTunes does actually say I have 1 available download and I have no idea how to remove this bogus item. It's causing me issues when I try to download something else on my MacBook. (It's only doing this on my MacBook).
Even when my iTunes is open it keeps bring up this message! Really annoying now.
I had this problem and worked with Apple Support to figure it out. Here's the solution I came up with.
https://www.quora.com/Ive-bought-a-movie-on-iTunes-but-it-wont-download-and-when -I-check-for-available-downloads-I-get-the-following-error-Unable-to-check-for-a vailable-downloads-The-network-connection-was-lost-What-do-I-do
There is a very easy fix for this. Go into your settings and make sure your iTunes is showing your purchase "in the cloud". then return to your music or movie page (whatever you are trying to download). Then simply click on the download icon for that purchase.
The problem seems to be that too many purchases get backed up on the download queue. I have that problem because until recently my internet connection was crap and I was skipping downloading all those stupid "extras" that come with movie purchases. I have a better connection now and I am slowly clearing those out (although I don actually want the extras and they just waste my downloads - but Apple being fairly stupid with this stuff I cant get rid of them).