I've hired a bike on a daily basis in the Algarve. It's similar to shop hire in much of Europe. Prices ranged from €7/day for a single-speed city bike up to I think €25 for some carbon bling. Bikes came with flat pedals so I didn't ask about anything else - I suspect they'd have SPDs around but if you want something unusual, it may be best to take your own along.
https://www.bicilet.com/regions/lisbon links some shops with prices. I don't think there's a city bike hire scheme like London/Paris yet.
I've not ridden in Lisbon, so take this with a bucket of salt (or salted cod?), but much of it is rather hilly, with many cobbled streets and there are tram tracks to deal with. Motorists seemed fairly cautious on minor roads (probably because they're dealing with hills, cobbles, trams and poor visibility) but as bad as any major city on the main routes. Cycle routes seem to stick to the coast and alongside the major routes inland (mainly Avenida da Liberdade / da República), with a big gap downtown. I expect it's fine if you take care planning routes.
Helmets are not compulsory and the road laws were updated in 2013 to help cycling. Cycling on some Lisbon routes has increased 17-fold in recent years.
I've written about my Algarve riding experience in the other place on
https://forum.cyclinguk.org/viewtopic.php?f=16&t=100699