S3 lifecycle policy object size limit 128KiB

You probably do not want to move ALL objects smaller than 128kB to Standard-IA, as S3 Standard-IA and S3 One Zone-IA storage have a minimum billable object size of 128 KB. Smaller objects may be stored but will always be charged for 128 KB of storage at the appropriate storage class rate.

Standard costs 0.023 per GB/Month and Standard-IA Costs 0.0125 per GB/Month (in US-EAST-1). This means that 128kB in Standard will cost 0.23 * (128*1000/1000^3) or $0.000002944 and the same 128kB in Standard-IA will cost $0.0000016. This means that any objects less than 70 bytes would be cheaper if you left them in Standard.

Then as Giovanni said, if they are 70 bytes or larger you can either manually transition them, or you can upload them directly to Standard-IA, but everything under 70 bytes you should leave in Standard.

Either you do a manual transition between storage classes or perform a direct upload to Standard-IA

If you plan to transition objects <128 Kb, you will always be charged for 128 KB of storage at the appropriate storage class rate in Standard-IA, One Zone - IA. If you want to reduce this transition cost and storage cost in Standard-IA, One Zone - IA, you can consider to compact small objects which is an effective way to optimize Storage costs. Here is a AWS Blog that explains how this is possible using AWS Lambda and AWS Step Function: https://aws.amazon.com/blogs/storage/optimizing-storage-costs-and-query-performance-by-compacting-small-objects/