Green’s Dictionary of Slang

shag v.2

[Gloucester dial. shag, to make off, to traipse around]

1. [1910s] (US Und.) to discover, to identify.

2. [1910s+] (US, also shag up) to chase; lit. and fig.

3. [1920s+] (US) to wander around; to walk, esp. slowly, whether through laziness or exhaustion.

4. [1930s-50s] (US black) to dance; thus shag artist, dancer.

5. [1930s–40s] to give someone a false impression.

6. [1940s+] to move fast.

7. [1950s] (US gang) to deliver.

8. [1960s+] to deal with.

9. [1960s+] to throw.

10. [1960s+] to obtain.

11. [1980s] (US teen) to tease, to harass.

In phrases

shag-lag (n.)

[1930s–40s] (US black) lying.