He is really bad at time management and even when he's late, shows no sign of being in a hurry.
He is a bad timekeeper and shows no sign of being in a hurry even when he's late.
「時間にルーズ」= bad at time management, bad at timekeeping, not good at time management・timekeeping/always turns up late
「急ぐ素振りもしない」= shows no sign of being in a hurry
「彼は時間にルーズで遅れてるのに急ぐ素振りもしない」= He is really bad at time management and even when he's late, shows no sign of being in a hurry. / He is a bad timekeeper and shows no sign of being in a hurry even when he's late.
He's always late and doesn't even bother to hurry.
例えば、 He's always late and doesn't even bother to hurry. 「彼はいつも遅刻して、急ぐ素振りすらしない」
また少し変えて、 He has no sense of time and never rushes even when he's late. 「彼は時間に全くルーズで、遅れていても決して急がない」 というようにも表現できます。
友達が毎回遅れる状況を強調する場合は、 He's never on time and acts like he's not in a rush even when he's late. 「彼はいつも時間通りに来ないし、遅れていても急いでいる様子がない」 という表現も使えます。