This is the 15335th most frequent Russian word.
потеряв
"Having lost."
"Потеряв" functions as a participle describing the state of having lost something (the keys).
Потеряв ключи, она не могла открыть дверь.
Having lost the keys, she couldn't open the door.
"Потеряв" serves to introduce the reason or condition that led to the ensuing action (starting his own business).
Потеряв работу, он решил открыть собственное дело.
After losing his job, he decided to start his own business.
Here, "потеряв" sets the condition (losing a close friend) which caused him to feel lonely.