Hi, well let's start by filling in a little more about who this Robert Lawrie is.
Robert Weir Lawrie 1881-1955 Born in Ratho, Midlothian, Scotland (?) Lived in/near Edinburgh (?) Dairy Farmer
I suggest you look carefully at the Passenger Manifests you found and check all the details to see if you have a "match."
I checked the Ellis Island site and found several Robert Lawrie's, but only these two (below) were of the right age. In looking at each of these passenger manifests, I could see the following details.
2 Ellis Island Records
#1 Robert Lawrie age 28 when traveling in 1909 = born about 1881. This Robert is from Kelty, Scotland. Married, departed from Londonberry. He is a miner, his mother is Ida Laughlin living in Blairs Terrace, Kelty. Robert is going to visit cousin J. Cook in Illinois.
#2 Robert Lawrie age 29 when traveling in 1911 = born about 1882. Currently living in Glasgow, Scotland. This Robert is single and he’s a waiter. He’s traveling to visit his aunt Mary Gilchrist in Pennsylvania.
So go on and on like that...checking the details and you may find an answer. If you zero in on a passenger manifest you're not sure of, you couldpost a transcription of it here. Volunteers won't be able to spot the details the way you can, so you will want to add information (such as where he was living in various years, wife's name, persons in the USA to whom he may have traveled, and so on.
I don't think the two Roberts I posted are the right Robert. Neither one of them is a dairy farmer. However, I do not know if he was a dairy farmer all his life....
You can see it will aid volunteers in helping you if you post more information.