Well first autolysis is practically unheard of on the homebrew level. It's also more about the yeast's cell wall rupturing than about dead yeast.
Just 3 weeks ago I kegged 5 gallons of pilsner and brewed 10 gallons the same day, poured half the yeast cake off to a second bucket and pumped the chilled pils wort into the buckets. I'll keg that 10 gallons tomorrow. It just so happens I used a new smack pack and starter for the first 5 gals because it was just time after using the previous slurry for about a year and at least 3-4 generations sometimes more.
Sometimes I split cakes like I described but more often is saved slurry. I'm not as picky as @sneezles61 I just leave a little beer on the cake, swirl it up and pour all that will fit into a qt mason jar and store it in the fridge. I don't generally use all at once, depends on it's age. Within a week or two I may pitch some without a starter, beyond that I make starters and pitch at high K.
Everyone creates their own process. This works for me. Your mileage may vary.