If you want to format the list of contacts in your Android 51 Lollipop device by first name first or last name first, you may do so from just one interface. It means, if you want to format the list by the first or last name, the list of contacts will be changed accordingly; either first names will come at the start or last one.
This is easier to change the format of the list of contacts by the first name or last name but if you need some help, do see the instructions.
Instructions
1: Tap the icon of the ‘Phone Dialer’ app at the Home screen of your Android 5.1 Lollipop device to open up the ‘Phone Dialer’ app screen. 
2: At the ‘Phone Dialer’ app screen, tap the settings button, placed on the top right corner of the screen. It will open up a popup menu.
3: Tap ‘Settings’ in the popup menu.
4: At the ‘Settings’ screen, tap the ‘General’. 
5: At the ‘General’ screen, see the current status of ‘Name format’ in the ‘Contact display options’ section is ‘Last name first’. 
6: If you want to change the format of the list of the contacts, tap the ‘Last name first’ under the ‘Name format’. It will open up a prompt where ‘Last name first’ is, currently, selected. 
7: Tap the ‘First name first’ to select in the prompt to change the format of the contact list. It will, instantly, take you back to the ‘General’ screen where the status of the ‘Name format’ is changed to the ‘First name first’.
8: See the current format of the contacts on the phone dialer app screen is ‘First name first’. 
That’s all!