I was inspired by Edmund's post to try some other lazy sorts. These are far from competitive to Java's timsort, but they are an interesting concept.
It is not possible to make timsort lazy because it uses insertion sort which does not work that way.
Insertion sort is very similar to selection sort. As in selection sort, after k passes through the array, the first k elements are in sorted order. For selection sort these are the k smallest elements, while in insertion sort they are whatever the first k elements were in the unsorted array.
A chunked lazy timsort might be attempted though. Another option might be to use selection sort instead, or use another compounded sort like introsort.
Update: I added an insertion sort and a chunked lazy timsort, without all the frills that make it actually run fast.