Crypto ATMs are great!
They are more and more popular these days and they are super convenient!
But make sure you understand what you are doing when you use them. You are purchasing Litecoin and waiting for the ATM company to send you the Litecoin.
There is no way to predict when that will happen.
It is not a block transaction (2.5 minute confirmation), instead they must take that transaction amount, batch it with other transactions and send them to the purchasers. They do this through their networks sometimes with poor Internet connections that can drop. Some are quick (within a few minutes) some take days.
So, this has nothing to do with Litewallet. Your copy of Litewallet is not managed by anyone other than you (your precious 12 words / seed). Litewallet checks the Litecoin network every few minutes and checks if your address balance has changed.
If you entered the Litewallet address to the crypto ATM, and the balance still zero, that means the crypto ATM hasn't yet sent the Litecoin to your address. Even if they gave you a receipt, the only way to really check for anyone is to check the Litecoin blockchain.
We use blockchain explorers to do that and they are free and pseudonymous. Just enter the LTC address and check and that is the most reliable source. (This is what Litewallet is doing as well)
Some popular block explorers are blockcypher.com, sochain.com