Suppose x has a duty to love y. Suppose A is an action such that if x loves y, then x is obligated to A. Does it logically follow x is obligated to A from the fact that x ought to love y?
In general not (this is a basic pattern of argument in Mark Murphy's divine authority book). After all, "x ought to G; if x Gs, then x ought to H; therefore x ought to H" is logically invalid. Besides, if x loves y, then x ought to say that x loves y when asked about it by y. But it is false that if merely ought to love y, then x ought to say that x loves y when asked about it by y; x should only say that if it is true.
But there may be particular cases where the inference is valid. For instance, it may be that if x has a duty to G, and H* is incompatible with and opposed to G, then x ought not to H*. Getting clear on the idea of how actions or attitudes can be opposed to one another is a non-trivial task, but there seem to be clear cases. Willing a basic evil to someone (say, death or stupidity or vice) seems to be opposed to love. So if x has a duty to love y, then x ought not to will a basic evil to y.
Are there some positive duties that logically follow from x's being obliged to love y? Consider the notion of a strongly loving action as a loving action that entails the presence of at least some love and that is such that whenever it is done, it is at least partially constitutive of love. The motivation is going to be essential to a strongly loving action (e.g., giving someone a glass of water can be a strongly loving action if guided by some motives, but not if it is guided by other motives). It seems that if x is obliged to love y, then because love is tied to action, x is obliged to engage in some strongly loving actions (what if x can't? but x always can--we can always at least wish well to people, and wishing is a kind of action, too).
Switching around quantifiers to get a stronger claim: Are there maybe some strongly loving actions that x is obliged to engage in? Presumably, yes--those actions refraining from which would be opposed to the love which is obligatory. What are those? It may depend on the kind of love that is obligatory between x and y. If y is God, and x is not God, obedience might be like that.