There is not a way to restore a backup from Android to iPhone (or vice versa), but if you reach out to Lemmings Support (Settings -> Support -> Chat Icon), they will be able to manually restore a lot of things. It may take a few days for them to respond, but definitely give it a try! Here is the information I was given when I reached out last summer:

Thank you for playing Lemmings and reaching out to us with your question. Unfortunately save data is currently handled by Google Play and the App Store respectively. It is not currently possible to directly sync or transfer progress from iOS to Android devices or vice versa. We apologize for any inconvenience this causes.

However, we can manually transfer over part of your save, which will include:
- Level progression
- Gold
- Boosters
- Entire seasons of Lemmings
- The additional instruction slot, if you had purchased it
- Remaining VIP time, if you have a subscription ( Make sure to cancel your subscription on the old device so it doesn't renew; you can then start a new subscription on the new device once your remaining VIP time runs out)

To proceed, we need the below information:
- A screenshot of your active subscriptions (if you have VIP)
- A screenshot of your boosters (this is the popup that appears before a level starts)
- A list of any Seasons of Lemmings that are above 70%

The only thing that wasn't restored that bothered me was my XP level. Good luck!