Please give the complete example if you are trying to use an analogy.  She was disqualified and lost CM post due to the conviction and not because she simply ceased to be an MLA.  I believe that an MLC can also be CM, K Rosaiah the present CM of Andhra Pradesh being an MLC.They should only enjoy the support of the majority.
https://en.wikipedia.org/wiki/Chief_Minister_%28India%29#Eligibility

My understanding uses the following examples:

First, holding the post of PM of India https://en.wikipedia.org/wiki/Prime_Minister_of_India#Eligibility
" be a member of the Lok Sabha or the Rajya Sabha. If the person chosen as the prime minister is neither a member of the Lok Sabha nor the Rajya Sabha at the time of selection, he must become a member of either of the houses within six months."

Second, our current MHRD, Ms Smriti Irani lost the MP elections from Amethi, Uttar Pradesh but was still appointed to the post.

So yes, the logic is simple. The EC member held the primary membership and this lapsed due to some reason. And the membership was then renewed.  I believe that the EC can take a decision to ratify the membership and amend the rules as well.

Hope this solves the dilemma. Now can we get back to work?