Lausanne is not the best city for bikes, due to all the hills, but a bike ride by the lakeside is very pleasant.
Attention: if you want to enter the public means of transport with your bike, you need to pay a ticket for the bike, otherwise you’ll pay a fine.
Renting a bike:
In Switzerland there is a bike renting system, called publibike with which you can rent a bike by the hour. There are plenty of bike stands in the UNIL and EPFL campus, and in other spots in the city.
Buying/Repairing a bike:
If you wish to buy a bike, you can find stores throughout the city and plenty second-hand offers in sites like anibis.ch or on facebook groups.
A very useful service is the point velo at EPFL (behind the INF building), where you can buy second-hand bikes for around 100 francs or repair your bikes for free or for a very small price.