Lustral, generic name Sertraline, is an SSRI antidepressant, and one of the best ones, with the fewest side effects.
You may notice some improvement within the first few weeks of the increase in dose. But this is individual. Some people may not notice because the effects are suttle.
But , just for your information, it has been found that with this class of medication there is actually an increase in growth in certain nerve cells in parts of the brain - this process can be ongoing with effects taking place in 6 months to a year. Areas of the brain are "rewired" over time when remaining of the medication, areas "that are important for thinking and feeling..." You may like to read this article for further details: http://www.sciencedaily.com/releases/2005/12/051220084704.htm
So, in other words, you can expect improvement to be continuous at least up to a year.
This is why, that some people after they go off the medications do well for some time, but may gradually begin to show their old symptoms of depression and/or anxiety. (This is because it does not appear that the growth effects are necessarily permanent when the medication is stopped)
I hope you find this info helpful and that it answered your question. But if you have further questions about this, please do reply to this post before rating me so that I may assist you until you are completely satisfied with your answer.