You can call Ego customer service at 1-855-EGO-5656 (1-855-346-5656) from 8:30AM - 8:00PM EST (Monday -
Friday) & 10:00AM - 6:00PM EST (Saturday & Sunday). They'll help you out.
I hate to state the obvious, but it's probably worth looking for the key. It's not all that small, and bright green. Even if it's outside somewhere it's just plastic, so it wouldn't be damaged by rain or dew.
There are only so many places you've been with your mower. Just retrace your steps. It's got to be there somewhere!