I'd say you're right about Lesser Coucal on this bird, given the shade of brown and also it seems to be streaked.
Beware that some juvenile Greaters can be fairly brown, but that is usually due to brown tips to black feathers so overall they appear darker than this, and are also a more reddish-chestnut tone rather than the straw colour on this bird. For example:
http://orientalbirdimages.org/search.php?Bird_Image_ID=31863&Bird_ID=462&Bird_Family_ID=&Location=
What I am less confident about is ageing this bird. Adult and First winter Lesser have a streaked brown winter plumage, very different from the summer adults. I think your bird is in this plumage, so could only be aged if you can see barred juvenile flight feathers.
For separating Lesser and Greater at distance, that's easy at this time of year when they have very different plumage. In summer, I usually look for streaking on the mantle/wings of Lesser, which is visible at quite a long distance. The upperparts of Lesser also look a shade paler, perhaps due to the streaking. Lesser tends to look slightly shorter-tailed and smaller-billed, but that can be hard to judge.
Habitat is also useful, at least in HK - Greater occur anywhere, but usually where there is lots of shrubby vegetation. Lesser mostly occurs in grassland or grassy marshes without many shrubs. There is some overlap though, so don't rely solely on this.