A1. This is something 3 year old me would have liked.
A2. This is something the 3 year old me would have liked.

B1. She doesn't particularly like sweets. But her sister, the three year old Amanda, enjoyed them very much.
B2. She doesn't particularly like sweets. But her sister, three year old Amanda, enjoyed them very much.

C1. The book was written by popular writer C.S. Lewis.
C2. The book was written by the popular writer C.S. Lewis.

Which sentences sound natural? And why?

Question

A1. This is something 3 year old me would have liked.
A2. This is something the 3 year old me would have liked.

B1. She doesn't particularly like sweets. But her sister, the three year old Amanda, enjoyed them very much.
B2. She doesn't particularly like sweets. But her sister, three year old Amanda, enjoyed them very much.

C1. The book was written by popular writer C.S. Lewis.
C2. The book was written by the popular writer C.S. Lewis.

Which sentences sound natural? And why?

Answer

Good question! In general, think about whether it would sound correct to use the definite article ('the') without the adjective.
In A2, if the adjective is '3-year-old', and we remove it, it doesn't sound correct to say 'This is something the me would have like'. So A1 sounds more correct.
In B1, it doesn't sound right to say 'her sister, the Amanda' so B2 sounds more correct. 
C1 and C2 are both correct. In English we can say, 'written by writer ...' or 'written by the writer ...'. The C1 construction is more common in journalistic writing, because it is shorter and more direct.