I forgot the photo
It depends on a lot of factors like the overall size of the tree, container or inground, the variety, etc.
From the number of fruits I would venture a guess that it is a Meyer. In general citrus are self thinning; so at least some of these will turn yellow and fall off. If it is a Meyer and a young tree, it will keep too many fruit to the detriment of tree growth. On my garden Meyers, when the fruits are on the end of the limb as these are, I would thin them at this point to no more than 8 or 10; later to 6 and later maybe to 3 or 4. A part of that depends on the strength of the limb. Meyers, and most lemons will bend but not break; but if the limb bends to the point of touching the ground it invites diseases and critters, so should be thinned or pruned to avoid that.
This could be any lemon. Lemons are prolific. My Santa Teresa lemon is as prolific as my Meyer. In fact, the poor tree is tipping to one side due to the fruit load. Also, Eureka, Lisbon and Italian lemons tend to produce clusters of fruit at the end of branches at the outside of the canopy (especially the Eureka), whereas Improved Meyer lemons tend to produce single or double fruits (sometimes clusters) all over the tree. Citrus trees in general tend to set more fruit than they can manage, and the extra fruit will drop off, as they are usually pretty good at self-thinning. Some young trees will drop all their fruits, as they establish themselves the first year or two, so that's not surprising. I would wait to see how the fruit sets. If your tree is very young (can't tell, as you didn't give us a photo of your entire tree), you can thin to just a few fruits, to give your tree a chance to establish itself. Lemons are extremely prolific fruit trees, and will flower multiple times and provide fruit in "rounds" over a long season, almost year 'round.
Thank you for the great advice john. It's a 2-3 yr container Meyer. How do I thin them? Should I cut below the lemon and squished cotton? Is it ok to prune while fruit is on the tree?
Don't thin them, yet, Suzy. Let the tree drop the fruit, first. If it doesn't drop enough, simply pull them off. You should leave a few for sure, you've had the tree long enough that it can support a decent amount.
Snip off the fruit stem to thin. As for pruning, the fewer leaves the fewer fruits the tree can support; other than that, I do my significant pruning twice per year at about a month before the primary bloom period and 6 months later. Prune citrus for shape, for esthetics, to trim back watersprouts to the canopy level, to remove crossing branches in the center, and to remove branches growing toward the ground; you can do that type pruning whenever you wish, remembering the caveat about fewer fruits with fewer leaves. Here's an example of what is definitely too much for one branch; this comes from a 3 year old tree inground on Macrophylla rootstock.
John that looks like what I have. Patty very very good info., big help. Thank you both for your help. I have 2 more clusters still white balls. One is very slow growing. The other is ready to pop. They are on ends also.
You have a Meyer, which is what John grows in very large quantities in Guatemala. I only have one tree, I can can barely keep up with the lemon production on this mature tree. My neighbors draw their blinds when they see me walking down the street with grocery bags :-) When the fruit are tiny - bebe size - you can pull them off easily. If they get larger, they are harder to pull off. John is right about snipping at that point (larger than golf balls). Be sure to fertilize regularly, as Meyers are just so prolific, they need a little "extra". Most lemons do.
If you leave them all, the tree will keep most of them... lets say 25; and next year it will produce 25; and the next year; and in 5 years, the tree will still be producing 25 lemons and will still be the same size.
Here is a photo of a typical California contain Meyer at 3 years.
Also, because it is a Meyer and produces so prodigiously, it needs a 3-1-2 NPK ratio; I used to say 6-2-4 until someone wisely pointed out to me it is the same. In my field Meyers (as Patty pointed out, I have 16,000 now) I use 18-6-12, specially formulated for me, with the minerals and micronutrients the Meyer needs, most notably Magnesium and Calcium.
Oh, and here are my Meyers at 2 years; tropical climate and Macrophylla root.
Wow, John you do have a lot of trees! Should I leave the babies and hope that they fall off or cut them? With the numbers that you gave me, were you talking about soil or fertilizer?
So what is your biggest problem (pest or disease) with running an orchard?
The 3-1-2; or 18-6-12 refers to the ratio N-P-K.
My biggest pest? I guess it would be ants and leafcutter ants; you have to stay on top of them constantly; if not the leafcutters can strip a tree overnight; and the regular ants bring citrus aphid.
Note that I do spray with Bayer Silvacur (fungicide) and Bayer Leverage (Imidacloprid insecticide) twice per year; they are both topically active and systemically active, so I don't have too many problems that I can't let the beneficials take care of.
I am a strict proponent of orchard sanitation, as with the close spacing we use, greasy spot can quickly become a problem if the orchard floor is not kept clean.