Here is a little tutorial going over 2 different ways to resize an image for Alamy
Resize an Image for Alamy, How-To - Adobe Photoshop Tutorial [In-Depth]
http://tutorvid.com/photoshop-tutorial/resize-an-image-for-alamy-how-to-in-depth/

AFAIK: Incremental enlargement made sense for ancient algorithms. Bicubic directly to target size does it much better.

You set longest edge to 5100 in LR and export !?   

Very hand tutorial for anyone submitting to Alamy.

Rgds

Oldhand

Copy the text below & save it as a text file called AlamyRes.js (or similar) in the PS scripts folder.

open image in PS, create a new action and then run the script (under file -> scripts). stop action recording (if you saved it somewhere else ie 'my docs' go to scripts and browse for the script, it will still work just dont move it afterwards )

now you have an action that will resize an image to exactly 48mb. If you select a group of files in bridge go to image processor you can run the action from there and resize batches of images.

#target photoshop
var targetMB=48;
var target=(targetMB*1024*1024)/3;
app.bringToFront();
docRef = app.activeDocument;
var width=docRef.width;
width.convert("px");
var height=docRef.height;
height.convert("px");
var ratio=(width/height)*1000;
var newHeight=new UnitValue(Math.floor(Math.sqrt((target*1000)/ratio)+0.5), "px");
var newWidth=new UnitValue(Math.floor(((newHeight*ratio)/1000)+0.5), "px");
var dpi=300;
docRef.resizeImage(newWidth, newHeight, dpi, ResampleMethod.BICUBICSMOOTHER);

For those who do not use PS - you can try size calculator @ http://statsmicro.com/resize