Putting Stryver in a sentence with the word love is as ridiculous as Stryver himself. The only person Stryver is in love with is himself, and the only thing Stryver is in love with is his own ambition. He doesn't belong in any discussion of love with Charles and Lucie. Sydney is another matter, and he's not part of any love triangle. Carton expressed his true feelings of love for Lucie once in words and once with his life--in between, he was nothing more than a rather sad and lonely family friend who was loved especially by Lucie's children. There is no love triangle here.
Since Charles Dickens' novel, A Tale of Two Cities, is replete with parallels among characters, it is easy for readers to become somewhat confused in the interplay of these characters, who are also rather flat and not fully developed.
However, Charles Darnay act as foils to each other. Remember that Darnay so closely resembles Carton that he is released from the charges of treason at his trial in the beginning of the novel. Carton later looks into a mirror and mutters to himself as he sees reflected the dissipated form of Darnay. Thus, feeling unworthy for her complete affections, Carton settles for a platonic relationship with Lucie, declaring his figurative, and later literal, undying devotion.
The scene in which Stryver, who "shoulders his way" in pronouncing his intentions to marry Miss Manette is a parody of a true courtship and meant to provide comic relief from the melodrama of the lives of Darnay and the Manettes. His self-serving disillusion of his power to allow Lucie to marry him as the worthy barrister sets him against the two men whose love is unselfish. Thus, his crass arrogance sets him apart from his "jackal," who is really a more worthy man.
Of course it is more of a love square if you believe that Stryver is in love with Lucie. Of course, it is more of an infatuation that passes when he realises he stands no hope. So perhaps it is better to describe it as a triangle as both Carton and Darnay love Lucie, but in no way are they rivals for her affection. Carton seems to recognise the hopelessness of his case and accepts the marriage of Lucie to Darnay. His love is more than merely romantic, as is proved by his final sacrifice at the end of the tale.
Lucie is married to Charles Darnay, and they have a daughter also named Lucie. Sydney Carton is the lawyer who greatly resembles Charles and who is very much in love with Lucie - so much so that he's willing to go to the guillotine to save Charles in order to keep Lucie happy.
I wouldn't call this a love triangle in the true sense of the phrase because these people aren't fighting amongst themselves, cheating on each other, etc. Lucie is faithful to Charles - Charles is faithful to Lucie - and because he knows he could never have offered her a good life like Charles could, Sydney did not pursue Lucie, other than to remain their friend until his death in Charles' place.
It's two intersecting triangles. Stryver with Darnay and Lucie. Carton with Lucie and Darnay. Darnay with Lucie. And Lucie with all of them.