Can I use Mantine's "Group Swim" attack to put one half of a Lugia LEGEND card in my hand?
Yes. Either half of the Lugia LEGEND card is still considered "a Water-type Pokemon", so you can search for it with Group Swim.
Source: HeartGold & SoulSilver FAQ (2010-02-11), PUI Rules Team (2010-02-11)

Relevant cards

Note: All applicable cards may not be listed below.
HGSS1_45