You can set it as a string, as in your example, but as you put the object in an array with [obj], you also need to select the index 0:
list.data[0]["limitstart"] = 24;
Or you can do it as a property:
list.data[0].limitstart = 24;
Working example.
For your correct output, you do not need to put objin an array:
var obj = {limit: '2', layout: 'getConversations'};
var list = {data: obj};
list.data.limitstart = 24;
console.debug(list.data);
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