*** Book Spoilers***
Remember that Lara was also technically still married to Pavel "Pasha" Antipov, although he abandoned her and their child and was living as Strelnikov. It is made much more clear in the book (the movie only hints at it) that Lara still loves Pasha, the man she married, her first love, and of course she would like to have him back. There is a passage after Strelinkov has released Zhivago where he reflects on the life he left behind. He was hoping, despite his new life, that could find his way back to Lara and Katya. And while Komorovsky has told Yuri that Strelnikov was captured and killed, after Zhivago sends Lara and Katya away with Komorovsky and is alone in Varykino, Pasha/Strelnikiov appears, looking for his wife and daughter. (This part was included in the 2002 miniseries). The two men have a long talk and reflect on their experiences and their mutual love for Lara. Zhivago asks him, "Do you have any idea how much she loved you?" It's a very touching and heartbreaking sequence. After Yuri goes to bed, Pasha kills himself. Although Lara does not see Yuri again (and is completely unaware that he was trying to catch up with her when he died), she does not believe that Pasha is dead, until Yevgraf confirms it.
And Yuri's friend Misha (who is not in the movie) is in love with Tonya but out of respect for Yuri and Tonya he does not act on his feelings and remains a confidante and friend to both.
So you could say that many lives are entangled, and both Yuri and Lara despite the deep bond and love they share, also have other loves.
Yuri did not leave Tonya of his own free will; he was forced to. Pasha left Lara, allowed her to believe that he may have been killed in action, and after his dreadful and horrible reign as Strelinkov, he wanted to get back to her but came to that realization too late. Yuri saw Lara and tried to reach her but died before that could happen; Lara searches for her daughter with Yuri, and then vanishes. So it's also about fate and circumstance. Yes, Yuri Zhivago loved both Lara and Tonya, just as Lara loved both Yuri and Pasha.
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