For surlie, you don't want anything in the lees but dead yeast cells. Anything else can rot and spoil the wine. Before you rack to secondary, stir the wine so the yeast are in suspension. Then let the wine settle for about 30 minutes and rack, leaving all the big stuff behind. The yeast will still be in suspension but the larger lees will have settled out.
Once you have racked, let the wine completely finish fermenting, then go ahead and add your stabilizing k-meta. (Some don't stabilize until after surlie is done, but in a home environment, you could be taking a change on the wine spoiling, depending on how long you do surlie.)
You can simply let the wine set on the lees and not stir, which takes longer for the wine to pick up the surlie characteristics, or you can also stir (battonage), which is the norm.
Stir (battonage) once per week; at the most twice per week. Generally it will take a week before the last stir's results have settled back to the bottom. Every week before you stir, taste the wine and decide when you have enough of the yeasty, biscuity, nutty flavor you want. Once you are satisfied, rack off the yeast sediment and begin the clearing process. It is typical to battonage for 6 to 8 weeks, depending on your individual taste.
Be mindful that surlie/battonage will greatly reduce any fruitiness that might have otherwise been present in the wine. Don't try it on a aromatic wine, like Riesling or a Gwerts. Only lite reds should be considered for this process and that not very often.
Good stuff!
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