In other words, Lance and Tommy are together for the benefit: Lance and Tommy cooperated in investigating Diaz before hitting Diaz. At the beginning of the new gang, Tommy needed Lance to gather people who belonged to the Vance family before (Ken was responsible for Tommy's legal inheritance of Diaz's mansion, and Eli Carrington was responsible for providing Tommy with information about the city's real estate, not to mention Tommy). When the gang reached a certain scale, Lance began to have friction because of the uneven distribution of Tommy's stolen goods (see the phone call in the middle and late game), so Lance and Tommy finally broke up. At this time, Sonny extended an olive branch to Tommy (presumably to let Lance control the evil business), which led Lance to make up his mind to break with Tommy.
Tommy risked his life to save Lance entirely out of interest, because after killing Diaz, people loyal to Diaz in Diaz gang may rebel (in fact, Tommy didn't fully accept Diaz's influence in 1986, Diaz also has influence in Colombia and Bahamas besides Sin City headquarters), and Lance also has a certain reputation and foundation in Sin City, so Lance will definitely not die. As for Tommy's sadness, it's not Lance who is sad, because Tommy said it himself when he killed Lance: Lance, you are on the wrong team. The tone is extremely contemptuous (thanks to R*' s production attitude). Who's Tommy Sade? Which is Sonny's old godfather? It's true that Sonny put Tommy in prison 15 years (actually Sonny had to explain it in detail in R* official website), but since Tommy didn't betray the Foley family in prison, he was willing to work for Foley after he got out of prison (Tommy came to Sin City without complaint, and Tommy could betray Foley and take him down in prison. Tommy is a core member of Freckley. It can be seen that he respected and feared Freckley before he had his own power (after he established power, Tommy remained nominally loyal to Freckley until Sonny brazenly attacked Tommy's industry).
Tommy and Sonny have a very good personal relationship. They are not only college classmates, but also comrades-in-arms who worked hard to start a business together (Tommy and Sonny are responsible for two-thirds of freire's becoming the overlord of Liberty City). So the relationship between Tommy and Sonny should be based on trust. So although Sonny put Tommy in prison for 15 years and tried to take Tommy's industrial profits (I don't know if the ending would change if Tommy turned over some profits instead of killing the people sent by Sonny), after Tommy killed Sonny, he still remembered the scene of two people struggling in Liberty City in the 1970s, so Tommy showed his sadness.