Lewis without a car?

I know there are buses that run from Stornoway to various sites on Lewis so you should be able to get to the main sites, although it might take some maneuvering. Keep in mind that buses don't run on Sunday (and many places are closed).

You also might try looking for a day tour. Callanish stones, the Blackhouse in Arnol, and the other main sites are all relatively close to each other on Lewis, so you could easily see them all in a half day or so.

Stornoway itself is very walkable and easy to get around in. Lews Castle is easily reached by foot from Stornoway so you wouldn't need public transportation for that.

ETA: Here are the bus timetables for Lewis: https://www.cne-siar.gov.uk/roads-travel-and-parking/public-transport/bus-services/lewis-bus-timetables/

Not my personal experience, but I met a young couple on the bus from Tarbet to Stornaway - I was on my way to a rental car and they were not. But I talked to them afterwards and they saw quite a bit by bus. I was impressed. The schedules Mardee linked to seemed to be accurate - I used the bus to see a bit of Harris.

Side note: I rented my car on Lewis from Car Hire Hebrides - did not bring one on the ferry. They have an office right at the harbor/bus station in Stornaway, as well as one at the airport. That might be an option.

We flew over last year for three days and Car Hire Hebrides was much more reasonable than other 'mainland' prices. Depending on what you're hoping to see, I think a car is indispensable (but we always get a car once we leave the city). Their one-way dropoff fees are a little less reasonable.

For both Arnol and Callanish you will need to use the W2, either way round the circle.