You will have to create a Entity Reference View to use as handler for doing the autocomplete lookup. Then you can add additional fields (such as last name) to the autocomplete results. This article outlines that process well enough:
https://www.cmsminds.com/blog/entity-reference-entity-reference-view-in-drupal-8/
If the field is a base field and is not available on the Manage form Display page, you will have to modify the entity class Lawyer::baseFieldDefinitions function. Specifically, you need to change the handler and set the form display settings. In your BaseFieldDefinition::create call:
->setSetting('handler', 'default')
Needs to change to this:
->setSetting('handler', 'views')
->setSetting('handler_settings', [
'view' => [
'view_name' => 'name_of_entity_reference_view',
'display_name' => 'name_of_view_display',
],
])
->setDisplayOptions('form', [
'type' => 'entity_reference_autocomplete',
'weight' => 2,
'settings' => [
'match_operator' => 'CONTAINS',
'size' => '60',
'autocomplete_type' => 'tags',
'placeholder' => '',
],
])
Alternatively, if you want to make base fields available in the UI, you can use this line to make the field available in the form display settings ui (and then export your form display settings as config:
->setDisplayConfigurable('form', TRUE);