I disagree with Billie.
For your first vote for Mayor of Lewisham choose any candidate/party you wish to support. With your second choice it is only worth voting for a party that has a good chance of being one of the top two or three - it is not for me to say which party that could be.
To use Billie's example: 'if you want the Lib Dems' first preference should be obvious, your second choice should be the party you think most likely to be in first or second place if the Lib Dems are not (possibly a choice between Labour and Conservative or possibly Green or possibly UKIP).

The results from the 2010 elections can be found at: http://www.lewisham.gov.uk/mayorandcounc...ction.aspx
What is shows (other than the result) is that over 100,000 people voted, 33,000 people voted for a party other than the top 2, and of these only 14,000 people picked a second choice that made it into the top two, which under this electoral system is a wasted vote by 19% of the electorate (plus another 4% wasted because they didn't understand/spoiled the ballot paper).

I would urge everybody to use their 1st and 2nd votes for mayor. And make sure you pick 3 names for local councillor (certainly no more than 3 otherwise all your selections will be rejected).