How to characterise lipophilicity?

I was provided with a drug compound which is filling a hydrophobic pocket. The R group is changed and effects on the potency was measured; $\ce{R = -H, -CH3, -CH2F}$ were tested. As expected, the more lipophilic group $\ce{-CH2F}$ had the smallest dissociation constant. However, the question went on to ask me to suggest other groups that could be tested. Investigating more lipophilic compounds would be wise, to further prove that the pocket is indeed hydrophobic.

It was suggested $\ce{-OCH3}$ as one of the groups that could be substituted for R. I am confused, because wouldn't the oxygen be able to form hydrogen bonds, making it hydrophilic rather than hydrophobic?

My question is, how do we classify a compound to be lipophilic? i.e. How do we know if the molecules form hydrogen bonds or not?