Electric bike battery question

I have a pair of electric bikes that I bought for my wife and I probably over 10 years ago. We almost never used them and they sat in the garage so they are practically brand new. Now I have more time and I want to start using them again, but the lead acid batteries are shot on them. So I'm doing some research on trying to get new batteries, but I wanted to upgrade to a Lithium Ion battery for both of them. They are more expensive, but a lot lighter and carry a better charge.

I stopped by a local bike shop that does electric bike conversions and talked to a young kid there. I told him what I had and what I wanted to do and he didn't think I could do it, but couldn't tell me exactly why. He didn't think you could use a Lithium Ion battery on a motor designed for Lead Acid. I'm no electrician so I have no idea if that's true or not. Anybody here with knowledge on this? The motor is a 24 volt .5 HP Currie motor. Currently it uses two lead acid 12 volt batteries linked together to make one 24 volt battery. Can I just get a 24 volt Lithium Ion battery and use it?