The most important thing to remember with these calves is you want to keep them happy. Stress kills and the quicker you can handle them, get them on fresh water and feed the better off they are going to be. The shot of LA will last 72 hours or about 3 days.
The reason why some people including us vaccinate as soon as they get off the truck is because if you pen them up and realize in a day or two they are sick its probably to late and even if you dont loose that calf your margines on that calf are tightning. Thus you vaccinate early as a pre-caughtion to help them get on fresh feed and water as quickly as possible.
Here is another tip, annually we run about 3000 stocker calves, 2000 of which are in a feedlot. Calves are stupid, when you put them in a pen it may take them a day or two to find where the feed and water is if they are just left alone. When we pen the cattle up they all seem to always go to the back except for the ones who found the ration in the bunk. These calves are stressed and in a new environment and just wonna stand around and ....well....whine. We ride the pens on horse and will push the calves up to the bunk and to the water trough so they know where it is(this does get them on feed quicker). We have noticed that with MOST sick calves that when we bring them out into the alley the first thing they do is go to the feed bunk, which means they havent been getting feed. When they get sick in the back of the pen they dont have enough heart to get up and go to the feed bunk. Even in smaller holding pens where you might keep a couple calves for a night, when you put them in there just walk them around really quietly and make sure they find the feed and water. Just work with your cattle be around them and they will tell you what they need. Even if you are bored someday get on your horse or just go stand in the middle of them and let them come acustom to you, you just might be amazed.
Hope some of this helps, good feed and water and mineral with the proper shots and you shouldnt have a problem.