I have a 2010 IS that I purchased in 2014 and replaced the battery last fall (2018) after owning it for 4 years. I put an Exide battery in it that had handles molded on the case. I used a saw to cut the handles off so I could put the sleeve on the battery.

My other car is an 2007 RX and that battery needs replacing every 2 years. Last time I replaced that battery, I bought one at Walmart and put it in. Hopefully it will last longer than the Lexus battery.

 

Yes there is a cover. Mine has one.

 

Here are pics and part # of the elusive battery cover. I had to take it out 12 years ago because it did not fit when installing an Optima Red Top.