Use GRC's SQRL for very secure (and unbelievably simple) login to LastPass. The actual authentication with SQRL involves the exchange of blocks of 256 bits of random garbage using public/private key technology. Intercepting and repeating all the traffic used during authentication is absolutely useless. All the details (including the ideas, the development, specifications and source code) are at grc.com/sqrl -- and it is free and open source.
If most sites used SQRL we would have far better security that would be really simple and fast. However, very few sites are smart enough to use SQRL.
However, even if SQRL were universal, LastPass would still be essential for handing all the other sensitive and private data - like credit card details, security questions (always use unique lies), Medicare numbers, insurance account numbers, copies of driver's licenses, copies of insurance cards.