Why don't you want to store your litecoins on cryptocurrency exchanges? Now it is not clear where it is better to store cryptocurrency, some exchanges provide better protection than many wallets. I can also leave a link to a review of the litecoin core wallet that I used several times.
If it's for bigger amounts, not ideal to store in any exchange.
You have no plans of trading them then don't store it on exchanges. But with OPs criteria, he's just going to store a few bucks of Litecoin and that amount isn't that much.
Well, still, I wouldn't say that store it on exchanges but if that's the amount and eventually you're going to trade that, your call.