The speaker is killing time, and in the process, hunting for romance. The title's phrase "on the make" gives it away: this is someone looking to pick up a stranger, and the poem is frank, even a little self-mocking, about how that works.
The first lines are casual, almost offhand. There's a wait, and love seems like a way to fill it. Then the speaker spots "a fine woman" and "play[s] at being thoughtful," holding a book ready as a prop. The word "play" matters. The speaker isn't actually absorbed in reading; the book is bait, a way to look interesting.
The final image is the sharpest. Speaking to "the beautifulest mouth," with its slightly awkward, almost childlike superlative, the speaker offers "a pretty lie." The mood is wry and a bit sheepish: charming, but aware of its own pretense. The poem seems to admit that flirting often means performing.