Lotus have indeed previously called it the i4 (for inline-4), the chap I was speaking to on the Lotus stand at Goodwood confirmed that it was a BMW complaint that caused them to move away from it.
An example of prior use, screenshot from my (May '23) order confirmation e-mail:
View attachment 48071
I guess the reason for using it initially is that i4 is a snappier designation than 4-cylinder when comparing to v6. Also, if they had called it Emira Turbo from the off this may have drawn comparisons with the 911 Turbo which may not have been good for expectation management, it's easier to transition now to including Turbo in the designation now the car is a known quantity.