Lawrence's scored a game high 23 points as Great Britain earned a 81-74 victory in Ljubljana, overturning an early 10-point deficit.
Coach Joe Prunty praised his younger players, in particular Lawrence and Myles Hesson, in what was effectively a knockout match.
But he concedes that Ukraine, who are coached by former NBA playcaller Mike Fratello, will pose even more difficult questions.
"We certainly know we have a tough task ahead of us," said Prunty. "They've played extremely well to this point, tomorrow is a huge game.
"I thought we did a great job on keeping Germany in check. On the offensive end, we got a lot of positive contributions from a lot of people.
"We had just seven turnovers which is a great effort. Andrew Lawrence played his best game, shot well, played some great defence.
"Myles Hesson was great again and Dan Clark played extremely hard, drawing a lot of attention out on the floor."
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- Mike Fratello