Lees is the yeast and debris that settle to the bottom of the primary fermenter.
When I replace I do scrap the old culture and start over. But as I said I have kept some alive for years.
When I feed I use a mixture of honey, water, and Malto which is an unfermented beer found at the grocery store with the Mexican foods (you may not have it oversees). I take the jar from the fridge - the yeast will be settled on the bottom. I pour off the clear fluid leaving the yeast, let it warm to room temperature and then add the water, honey, Malto mixture and swirl the jar to mix the yeast and put back into the fridge.
To use for a mead, I take the jar out of the fridge and feed as above but do not put back into the fridge. When it is fermenting I swirl to mix and pour half into another sterile jar. Feed the first jar again and place back into the fridge. To the second jar add a honey water mixture and a little nutrient - fill almost to the top of the jar. When it is fermenting vigorously I pour it into the mead.