A product will show as "Sold Out" when a products inventory has reached 0.
If the inventory value in Lightspeed is greater than 0 then first check on is the timestamp of the product. If the timestamp has not been updated then Lightspeed hasn't actively notified Channels a value has changed. In the following image, this product has a timestamp that was modified "4/23/2013".
Any inventory adjustments or PO actions that are performed in Lightspeed will not automatically modify the timestamp on a product card. The Nightly Inventory Sync will automatically update inventory values that differ from those in Channels if no other action is taken.
To force an inventory update on a product before the nightly sync, the product card will need to be updated.