I will argue that love does not lend anything to the LFW proponent’s case. Either what is meant is love is an action and is really a species of the argument from moral responsibility or love is parsed out as something that is descriptive of a mental, emotional or volitional state. If the former, then the compatibilist answer is no different to their answer to the general question of free will and moral responsibility. If the latter, then there is no sense in which love requires LFW.
Briefly, the compatibilist conception of free will is most commonly associated with volition. Human agent, S, freely chooses an action, A, if and only if S carries out A according to S’s volition and S is not coerced to carry it out A. This conception of free will, the compatibilist will argue, is both consistent with experience and is the necessary condition for moral responsibility. S is morally responsible for A iff S carried out A willingly and S is not coerced. Of course, the LFW proponent will be unsatisfied with this, but that is beside the point. Given, the compatibilist conception of free will, the LFW proponent does not make an additional argument by suggesting that love would not be possible if compatibilist free will is true. Rather, the argument from love reduces to the argument about the nature of free will and moral responsibility.
Perhaps the most difficult thing to do is figure out what we mean by “love.” There are, it should be conceded, a plethora of options. Some have even described the nature of love as ineffable. Well, perhaps we could start with some mundane statements someone might say. Let’s say, for example, the following are true of me:
(1) I love pancakes
(2) I love writing philosophy essays
(3) I love my Chihuahua 
(4) I love my wife
(5) I love God
What do we mean by love in these cases? What is it that libertarian free will is necessary for? Take (1). Is the love I have for pancakes only possible if I libertarianly choose to love pancakes? It does not appear so. If I love pancakes without choosing to love pancakes, then I don’t seem to require LFW to love them. Loving pancakes seems compatible with being determined to love pancakes because the kind of love in question is a matter of liking something a lot. Whether my tastes are predetermined or not makes no difference to the fact that I like pancakes very much.
(2) is a question of value. I value writing philosophy papers because it is what the Lord has given me to do in life. I am glorifying him and trying to benefit others. The kind of love in question has to do with valuing some way to spend my time because it is fulfilling. Does this require LFW? Not necessarily. It is possible that I was determined to find myself fulfilled by writing philosophy papers. Fulfillment doesn’t seem to logically or causally (or any other way) require LFW.
(3) How do I really love my Chihuahua? It might be something like taste. "A Chihuahua is my kind of dog." Or maybe value. "I value my Chihuahua because time with my Chihuahua is fulfilling" or perhaps my Chihuahua used to belong to Paris Hilton. That doesn’t sound quite right either. I value the Chihuahua for something intrinsic to the Chihuahua not merely for the value she has. So perhaps there is something like caring for the wellbeing of my Chihuahua. "I care-love my Chihuahua." I want my Chihuahua to be blissfully happy and pampered. If so, there is nothing extra that necessitates LFW in order to desire the the well being of my Chihuahua. If, on the other hand, what is meant by care-love is some set of duties I carry out in order to help my Chihuahua flourish, then those duties are actions and the argument returns to one about moral responsibility.
(4) suggests some love that is beyond care. There is more than affection, taste, or desire for the other’s well-being involved in a marriage. First, there is something like deep companionship and personal connection. Again, there is no obvious sense in which companionship requires LFW. Being predetermined to find companionship in another does not render companionship somehow meaningless. Again, if it is a description of a state of affairs, then there is no necessary relationship between the state of affairs and LFW. To find oneself in a state of personal intimacy with one's wife is not something that requires LFW.
However, in marriage there is commitment. What is commitment? At least, we should say that commitment is an acknowledged and articulated set of promises to fulfill certain duties for the other person: remain faithful, honor, protect. These are duties of marriage that entail choosing to act in a certain way to maintain the marriage. But then, if love is a set of duties performed by actions, then love is a species of actions. If this is what is in mind, then the compatibilistic answer remains the same. Human actions are free iff they are in accord with the desire of the agent and not coerced. The same is true of love. Human loving actions are free iff they are according to the agent’s desire and are not coerced. But, again, this is an argument about the nature of free will and morally responsible actions not about love per se.
(5) I think it is becoming clear that love, as far as we have defined it, is compatible with compatibilistic free will. And this is true of love for God. If by love for God we mean that we behold his beauty and are compelled to love him, then that does not necessitate LFW. If we mean that we love God if by obeying him (“if you love me, you will obey my commandments” John 14:15), then what we mean is that we obey him by acting according to his commands. And action is carried out according to the compatibilistic free will we, as humans, have.
I have argued that given the compatibilist free will with regard to human actions, love does not add anything extra to the LFW argument. Either love is defined as some species of a state of affairs or as a human action. If it is some mental or emotional state of affairs, then one’s version of free will is irrelevant. If it is a human action, then the argument is reduced to an argument about the nature of free will or the necessary conditions for moral responsibility.
 The doctrine of predestination is often described this way. God forces his people to love him since they had no real choice in the matter.
 The following rough categories I got from Bennett Helm, "Love", The Stanford Encyclopedia of Philosophy (Fall 2013 Edition), Edward N. Zalta (ed.), http://plato.stanford.edu/archives/fall2013/entries/love.
 This is false (the rest are true). I do not like Chihuahuas and I do not own one and, unless my wife wants one, I will never own one. If I have to own a Chihuahua, it will be because I love my wife. It is unlikely I will ever love my Chihuahua.