Can you fly to the us from another country if you lost your green card?

In theory, you could do an ESTA form online if you are from a Visa Waiver country. However, the INS will scan you at Immigration and know you have been resident so you will have some explaining to do. You could then explain you have lost your Green Card and give them a telephone number of the company you wrok for and they could verify you were in the US legally. They should let you in but you really would need to apply for a replacement acrd immediately.