It's incredibly competitive to get a training contract and you would have little chance of doing so unless you have very good A levels (many law firms require a minumum of ABB, for example) and went to a well respected University. If you are sure about Law, you would have far more chance of getting a training contract if you studied at Liverpool rather than Lincoln.
My advice would be to put Liverpool first and work as hard as you can at achieving the highest grades possible. If you don't achieve such high grades, maybe go to Lincoln instead, but be aware that you will struggle to become a solicitor (let alone barrister, which is even more competitive) if your grades are any worse than ABC. This being the case, you could always consider asking to switch to a different subject if you do particularly well in that one subject at A level or if you find that you aren't enjoying Law when the course begins.