I would like to use the second conditional to express something is unlikely to happen.
The problem is this unlikely condition is about the future. Is it still ok to say:
If I won the lottery next week, I would buy a new car.
If I won the lottery next week, (then) I would buy a new car.
If the condition (win the lottery) is considered improbable or counterfactual, yes you can express it by using the 'past tense form' in the if-clause and using 'would' in the then-clause. This is the so-called second conditional.
So your sentence is okay; but it means that you (a) believe the likelihood of winning the the lottery to be improbable or even (b) counter to fact.
The difference in the two are illustrated by the following pair of sentences (these are examples of the above two situations):
1 I could win the lottery next week, but it is highly improbable since I bought only one ticket and therefore my chances to win are slim to none, and I also happen to be am an extremely unlucky person, and no one in my family has ever won it and probably no one ever will... etc.
2 I could win the lottery next week, if I actually bought a ticket and tried, but since I am not doing that there is no way I can win (my winning is counter to fact).
However, if you are making a prediction about the future, you can just use the present tense in the if-clause and the future tense in the then-clause:
If I win the lottery next week, then I I'll buy a new car.
You are "predicting" (saying what you will do in the future) what? You are predicting that you will buy a new car but it is conditioned on you winning the lottery.
Your odds of winning may still be extremely low, because you bought only one ticket and etc, and so there is not much difference, really, between this 'future real conditional' and the second conditional discussed above.
Another example: friends are playing poker. Sam has lost a lot of money and the only way he can win back his money is if he wins the next six rounds, which will be played tomorrow (in the future).
Now, his friend and fellow poker player Rick can say either:
If you won six rounds in a row tomorrow, you would be extremely lucky.
Rick views the event has highly improbable. The sentence takes the form of the second conditional.
Or
If you win six rounds in a row tomorrow, you will be extremely lucky.
Rick views the event as highly improbable. But the sentence is cast in the 'future real conditional' or 'predictive conditional'. Rick is being "predictive" about Sam being extremely lucky and this is conditioned on Sam winning six rounds.
A counter-to-fact example for the poker players would be
If you won six rounds in a row next week, you would be really lucky indeed (since we are playing only four rounds).
See the Wikipedia article on conditionals for an extended discussion. Part of this answer is based on information contained in it.
The sentence makes sense to me as a native speaker, and these sources on second conditionals use such phrasing:
https://www.englishclub.com/grammar/verbs-conditional_3.htm
http://www.englishpage.com/conditional/futureconditional.html
Nope. The "next week" part throws everything out of whack.
If I win the lottery next week, I'll buy a new car.
If I ever won the lottery, I'd definitely buy a new car.
Should I ever win the lottery, I'll definitely consider buying a new car.
Had I won the lottery last week, I would have bought a new car first and foremost.
Suggested by Euan M:
If I were to win the lottery next week, I would...
or, a completely and irrevocably formal version:
Were I to win the lottery next week, I would ...
Here's a pretty decent page on conditionals:
http://grammar.ccc.commnet.edu/grammar/conditional2.htm
Yep, it's true. Put "if I ever won the lottery" in quotes and google it. Half of the 30,000 or so results will refer to fiction written in the past tense; the other half, though, is casual everyday talk in the present tense. Go figure, right?