On day 2 when you sell 50K worth of options yes you will immediately have 1lk to trade with, and will be available in realtime.
But here is one thing to remember, of this 1lk , 50k is free cash and 50k is cash from the sales you have made.
In case you hold entire 1lk of options for overnight, (50k free cash + 50 K which is still not realized (proceeds from sale of options is realized on T+1 day basis)).
So exchange would charge a tiny short margin penalty on this 50k, i.e if you hold the position for overnight.