One of the key concepts behind Lean is to eliminate wastage. You can apply this wastage elimination to all the processes within your project, including the daily stand-up meetings.
One key area where wastage can occur during the daily stand-up meeting is when it comes to discussing issues or blockers. Granted, some issues benefit from the input of the whole team. But be careful that you are not wasting the teams time by discussing issues within the whole team when only specific members need to be involved.
One technique you can use is to write the name of each issue on a whiteboard (or using post-it notes) and then next to the issue, identify who needs to be involved. After the stand-up meeting has finished, you can have a series of quick meetings for each issue with just the relevant people. And meanwhile, the rest of the team can carry on being productive.