Can you beat the suicide mission in mass effect 2 without upgrading the normandy?

i really like how my guy turned out, so i want to transfer him to m.e.3, and have all my squad mates survive. my friend told me to upgrade the ship or im screwed, but i don't have enough lithium(?) to upgrade a single thing. im really new to this game so i didnt no about that. do i absolutely need upgrades, or can i do it without, while still beeting and not loosing anyone.