Make sure that Google Fit is either preinstalled - otherwise download it.
In order to connect Lifesum and Google Fit please click on Profile on the bottom tab bar in your Diary. Then on the next page on the gear symbol. You will then see the option Automatic Tracking on the following page.
Tap on Automatic Tracking.
There you'll see a Google Fit box with a green Connect button. Tap on the button to connect to Google Fit and follow the instructions.