lay something up—
1. (also: lay something by) save or store smth. for future use:
- The power stations are laying up their usual supplies of coal.
2. (of a car, boat, etc.) take out of use (for repairs, etc.):
- At the end of the season, all the boats are formally laid up in the harbor.
put something up—
1. build smth.; place smth. in position:
- You have to put up a fence one foot away from the property line.
2. show smth. such as a notice in a public place:
- The examination results will be put up on this board tomorrow.
3. (of cost, taxes, etc.) increase or raise:
- These rents are fixed and cannot be put up.
4. pack smth.:
- She put up a parcel for her daughter who was away at college.
5. offer opposition:
- They were looking for an excuse to stop fighting, because neither one of them put up an argument.
6. offer smth. for sale:
- After grandmother’s death, the furniture was put up for sale.
7. = lay something up 2:
- We had to put the car up for the winter, it was not fit to drive in snow.
Note: The expression does not fully correlate in meaning with the phrase set something up—
1. = put something up 1:
- Does any of you know how to set up a tent?
2. establish an organization:
- A special committee has been set up to examine the details of the suggestion.
3. (Sport) reach a new record:
- The young swimmer has set up a new fast time for the backstroke.
4. place drinks or glasses ready:
- Will you set up the drinks while I look after the food?
5. cause pain or infection:
- This wet weather sets up the ache in my old wound.
6. produce a loud noise:
- The crowd set up a shout as the winner neared the post.