It is important to note that the writer emphasizes Linda "is neither disorganised nor innumerate", so such a person normally should not have any problem talking about her finances with numbers, but the fact is she gets confused discussing them. Pay attention to the contradiction here.
"Lose" here means "to make someone confused, to cause someone to be lost in something." When in a conversation you feel the other party is confusing, you can tell them: "You've lost me there." This is a common English idiom. Macmillan Dictionary:
to make someone confused when you are trying to explain something to them
I’m sorry, you’ve lost me there. Who’s Andrew?
The sentence at issue tells you Linda is put in a confused state of mind by a question about her finances. She is hard pressed to get her finances straight and come up with an accurate answer if she is presented with such a question. Here she is not necessarily confused by the questioner, but rather by the mess of a situation. So the sentence means
Although Linda (a 54-year-old event consultant in Los Angeles) knows math and is not disorganized, if you ask her about her finances, you will make her confused for two hours.
"Two hours" here is a figure of speech, not to be taken literally. This Economist article describes how confusing and troublesome money management is for ordinary middle-class people. That is why if you ask one of them about their finances, they will be lost in the numbers.
The definition I cite itself is a figure of speech of "lose". When people say "You've lost me", they mean "I am no longer with you in the conversation." That is what the idiom "lose someone in a conversation" means.
Another answer states "lose" here "means that you'll lose her in the discussion." I don't disagree with this. This is a more literal understanding of the word "lose".