What region?

9b Sacramento foothills, occasional winter temps below 25 degrees F, frequent summer temps over 100 degrees F. Low humidity.

These are some trees local nurseries mentioned.

pink velour crepe myrtle

purple pony plum tree

red tip photinia

carolina cherry laurel

pineapple guava

zelkova city sprite

carolina floral dwarf

Of the first three, the Vitex, Chaste Tree, is most suited to your climate. Nothing on either list qualifies as a shade tree. Most are large shrubs that can be TRAINED to small tree form. From the second list, the zelkova and crepe myrtle followed by the plum have a more natural small tree form.

So Zelkova or crepe myrtle sound best.

Any other suggestions not on the list based on the space requirements and climate?

'Very small lots' is not sufficiently descriptive of the actual space involved. It also says nothing about what else is happening in and around this space. Sun/shade/soil/maintenance needs, actual city rules and design aesthetic all come in to play when selecting plants. So no other suggestions at this point.

A lot that looks like this with about 10ft between the house foundation and the curb.

Trees would be planted in the grass

Goodness. If the city is requiring two trees be planted in the strips of grass in front of these houses with the choices you have provided, your neighborhood is being set up for major horticultural and design malfeasance. There is going to be a whole lot of ugly going on.

What you need here are columnar and fastigiate tree forms. This link has a short list of options to check for suitability. Ask the nursery people again about plants with this particular small tree form.

Trees, Shade, Columnar or Fastigiate (uaex.edu)

Here are some examples with trees.

What kind of trees are these?

Purple leaf plums. Lawns in first shot are deeper than 10' and trees have in addition been "stripped" (lower branches removed to an excessive degree) in order to make them fit within the setting.

While those in the second shot are simply too young to have exceeded the planting space.

Yet.

There is already a whole lot of ugly going on.

I think the first picture has a lot that‘s around 6 or 7 feet deep

Are there purple leaf plum dwarf varieties that stay small enough for those lots?

Don’t dwarf Japanese maple trees have similar look?

10' or 6'-7' - in either case these are dimensions suitable for accommodation of shrubs.