Receiving payment on Lightning Network with LNBig as initial funder?
In principle what you do should work. However there is a subtle but important feature in the lightning network protocol (meaning this is with every implementation) which we call the channel reserve. 

If you want to send money along a channel your node has to keep at least 1% of the channel capacity as a reserve / collateral to protect your channel partner in case you try to steal funds.

Let's say lnbig opened a 1 million Satoshi channel with you. As long as you do not have 10 thousand Satoshi on your side you will not be able to send money. If you have 11 thousand Satoshi in such a channel you can send up to 1000 Satoshi because you have to keep above 10000.