No. "I almost lost everything I own" means that you didn't lose anything at all, but you were in a situation in which it was very likely that you might lose everything you own. "I have lost almost everything I own" means that you did indeed lose most of your belongings.

Here's an example: I have a ten dollar bill. I accidently drop it off a bridge, but I manage to catch it before it falls out of reach. I almost lost all my money. I have ten one dollar bills. I'm very careless, and somehow lose 9 dollars. I've lost almost all my money.