A bike on a smart trainer still benefits from oil on the chain. But the floor pads under my bike still retain half the oil I last put on the chain. So, any recommendation for a good brand of oil for a chain that will only ever spend its life being used for indoor trainer (ie. high cling, low shed).
On my indoor-only trainer mule I use Squirt wax. This "bike" lives in a clean upstairs "gym room" so I don't want oil spray flicking off that I might walk/transfer around the house and I need to be able to do drivetrain cleaning in situ without creating much mess. With wax, instead of fine spray, you get a bunch of grey/black sticky waxy bits that fall off under the bike, and I have a "tray" positioned beneath the drivetrain to collect these.
For ongoing maintenance I quickly wipe the waxed chain once a week/fortnight using a rag wetted with biodegradable bike cleaner (non-solvent based!), then reapply a bit more Squirt, ready for use the next day after it's dried. And I clean all the shedded waxy blobs off the chainstay and "tray" underneath.
I've just replaced the chain after nearly 2 years usage, and did a full de-grease on the new chain prior to the first Squirt application. Did a slightly cut-down version of these lengthy steps, which was a bit of a faff but a once-only job:
https://moltenspeedwax.com/pages/clean-your-chainIME, wax makes for a cleaner indoor setup and ongoing maintenance than if I was to use my regular outdoor wet lube, and gives a very quiet, smooth drivetrain. Squirt is a lazy man's waxing regime compared to the people dunking their chains in the molten stuff. The easier life suits me.
NB this Squirt wax lubing regime is completely different to the one I use on the outdoor bikes. And if my trainer bike was in a garage or shed where I'd not be bothered about the mess I'd just use my regular outdoor wet lube.