Lists Comparison (Stacked & Keeping order)

I also think you have a problem with multiple solutions and/or undefined optimization.  You could easily come up with solutions that are likely far from optimal:  ABCDEF could match with BCDEFA in 2 ways:

A_B_C_D_E_F
x _B_C_D_E_F_A

or

x _x_x_ x_x_A_B_C_D_E_F
B_C_D_E_F_A

The former being much "better" match but I don't believe you have any 'rule' why the latter isn't a valid solution.  That said, I didn't break down your existing solution to see if it checks for that but it seams to be 'single path' iterative based so I don't think so.  we also know excel works with arrays more efficiently.  I have the following start that I feel could be useful but maybe you already tried and couldn't get further.  So on your sample sheet I took the 1st 'DEMO' and put the 2nd col into a row and found the matix of matches (shown using complex #s for row, column.  The last 2 columns (V & W) use those matches and sort the 'real'/rows based on the 'imaginary'/cols and then the reverse.  Any 'path' that increases both the row and column is a potential solution, so w/r to the 2 final columns any monotonically increasing set would be a potential solution of matching values (except these :

in this case I see 4 (non-trivial, i.e. sequences that do not exclude possible matches in between) match solutions:

2+3i, 6+5i, 8+6i, 9+9i
2+3i, 6+5i, 7+10i
2+3i, 5+8i, 6+9i, 7+10i
2+3i, 5+8i, 9+9i

So although this step makes it much easier for me to find those solutions I'm not seeing a way to functionally do it.  Like it would be nice if there was a trick using MMULT or something to give potential solutions and then use the one that is the longest.  In THIS case you can easily go row by row or column by column to find the 2 'best' solutions but that would NOT be the case if the 1st column ended with JUL and the 2nd column ended with MAY as those would have to be 'skipped' in each corresponsing case to avoid the 2 match solution.

Thanks but the original order of array elements should remain same, that is the requirement.

So yes, the same elements must align in same row, but within each array, the sequence of elements must remain same in output.

Such type of comparison is useful, e.g. in comparing text documents, like code comparisons (which line got deleted/added/remained same). Other use cases could be comparison of multiple products features and specifications grouped by categories from top to bottom.

I could make the solution but it is slow.

There are approaches that would expand to 3 or more columns provided the 'months' can be interpreted as dates with a natural sort order (otherwise I suspect the results are ambiguous).  For example

corresponds to your initial problem but starting with Excel dates rather than the abbreviated names of months.  The intermediate step is a combined list of tagged dates.

= LET(
    taggedA,  EXPAND(listA,,2,"List A"),
    taggedB,  EXPAND(listB,,2,"List B"),
    combined, SORT(VSTACK(taggedA, taggedB)),
    group,    TAKE(combined,,-1),
    month,    TAKE(combined,,1),
    DROP(PIVOTBY(month, group, month, MAX,,0,,0),,1)
  )

This is fast, but it required additional structure within your data.

In attached Excel file, 3-Lists comparison function implemented - but the calc is so slow that Excel becomes unresponsive. Have set the calculation to Manual.

Looking for better ideas for this function which is faster and practical.

Thanks in advance.