She gave me a steady look and walked out of the meeting room.

Literal

She [topic-は] firm gaze [with-で] me [object-を] saw [then-て], meeting-room [path-を] exited.

しっかりした (the past attributive of しっかりする, 'be firm/steady') functions here as 'firm, steady, resolute' — applied to her 視線 ('gaze, line of sight'), it paints a look of unwavering composure, the kind of resolved gaze that closes a charged moment. The で marks the manner — 'with a firm gaze.' The verb 見る ('see, look') chains via the te-form 見て into 出る ('exit'), sequencing the two actions: she looked, then left. 視線 is the formal noun for a line of sight, distinct from the more colloquial verbal 見ること; using it raises the description to a slightly literary register often found in fiction or news prose. The を on 会議室 marks the place exited from — another instance of を with motion verbs.