I am guessing the answer to this is NO as it has been five days since I sent the funds, but can I send Lite-coins from my coin-base account to by ELECTRUM wallet? Also if not are there any services that provide cold storage of various types of crypto currencies not just one, like only BTC or only ETH...?
Thanks
Sorry, one step back, can you tell us what happened?
From what i can tell, you bought litecoins from coinbase... So far, so good...
But when you sent them to electrum, i do hope you mean "Electrum Litecoin" and not Electrum? Electrum itself is a bitcoin wallet. It has been cloned by somebody and adapted for litecoin, so i hope you used this version, and not the original one.
IF you used "Electrum Litecoin", you should be able to fund your electrum address from your coinbase account without any problems. If something went wrong, posting a txid might help us find out what happened.
As for cold storage of many types of coins, i recommand either a trezor or ledger nano S. Both these hardware wallets cost less than $100 (excluding shipping) and support a limited amount of altcoins. You'll have to search their FAQ's to find out which altcoins they support.