I wouldn't pull any lemons off, the tree will decide on it's own how many lemons it can handle. Actually it looks like yours has already gone through that process, it happens during bloom time and then again once the fruit is about pea sized. I would leave it alone and wait for the fruit to mature IMHO.
Evan

you will want to remove a bit more of the grass and apply a good application of fertilizer. meyer are heavy feeders and this one is showing sign of deficiency.

Mike

the amount of fruit looks about right.

i agree with Mike, remove the grass from around the tree, add some mulch and some fertilizer.

jkom51 What a gorgeous tree. Thanks for posting that photo. I would have had no idea what my tree could do had I not seen that photo. Amazing possibilities. Patricia

Debra,

Your Meyer is seriously underfed; and with that size tree and that condition I would take off at least half the fruit. When the fruit is greener than the leaves, you know you have fertility problems. Also, a young Meyer (under 4 years) will NOT thin itself; it will keep too many fruits and "forget" to grow. If you leave all those fruits, next year it will have an equal number; and the next year the same; and in 5 years it will still be producing the same number and the tree will still be the same size. Once your tree gets older, say 4-5 years, it will do a pretty good job of self thinning.
The next issue is that your tree appears to be staked; that is a recipe for disaster. Try lowering the ties 3 inches every 2 months until you can remove them completely. Citrus do not need support; staking only prevents the trunk from thickening naturally.