There are a few simple things you can do to minimise any health risks from lead pipes, without having to replace the actual pipes.
Run the water: when you wake up in the morning, run the cold tap in the kitchen to flush out any water that has been standing in the pipes overnight. A sink full should do it. You can always use this water for your plants.
Flush the loo: flushing the loo will also do the job of clearing any water that has been standing in the pipes overnight.
Use the kitchen tap: only use water from the cold tap in the kitchen for drinks and food preparation. You can find more tips here.