As you stated, observations from the same individual will be correlated, as will observations from the same leg. You can estimate and compare the strength of these correlations using a mixed effects model.
Walking condition is a fixed effect. Leg is a random effect nested within subjects, unless for some reason you believe there is a left-right leg difference, in which case you could model it as a crossed effect within subjects. The nested model can be written:
$$ y_{ijk} = \mu + c_j + s_i + e_{ik} + \epsilon_{ijk} $$
where $i = 1,2,\ldots,15$ indexes subjects, $j = 1,2,\ldots, 5$ indexes the walking condition, and $k = 1,2$ indexes left and right legs. $c_j$ is fixed, $s_i \sim N(0, \sigma_s^2)$, $e_{ik} \sim N(0, \sigma_e^2)$, and $\epsilon_{ijk} \sim N(0, \sigma^2)$. Since the total variance is $\sigma_s^2 + \sigma_e^2 + \sigma^2$, the correlation between measurements on the same subject is $\sigma_s^2 / (\sigma_s^2 + \sigma_e^2 + \sigma^2)$ and on the same leg is $\sigma_e^2 / (\sigma_s^2 + \sigma_e^2 + \sigma^2)$. You can compare these two numbers in your analysis to discuss the relative magnitude of the two correlations. Another way to think about this approach is that you are comparing the amount of variation across subjects to the amount of variation across left and right legs.
Finally, a likelihood ratio test will tell you whether condition is a significant predictor of $y$, given the nested structure of your data. If you expect variance terms to depend on the walking condition, the model will become more complicated.
