I would check it to make sure the different lemons are not growing out of separate branches. One variety could be rootstock.

The rootstock taking over would be a common explanation. Check where the branches bearing the strange 'lemons' grow from. Usually it is not hard to distinguish the boundary between rootstock and scion as the bark tends to change in colour and/or there is often an abrupt change in thickness (depending on the combination).

They look to have been infected by broad mite, when the lemon was small. They should be fine inside; if you have doubts, cut one open and see.

Agree. It's damage from a rust mite. But understand that, with the damaged peel, the affected fruits tend to dry out more rapidly than normal.

See http://ipm.ucanr.edu/PMG/GARDEN/FRUIT/PESTS/citrustmite.html

When I gardened in Long each, CA, my lemon tree had the same damage but only now and then. Never treated the tree because it was unimportant in a home garden. The story is different for a commercial producer who must have perfect fruit or s/he loses money.