No, LRT is not needed on Finch East. It'd be a huge waste of a billion dollars that replaces a functional bus route with something that the TTC has proven to be not fully competent at operating, something that will result in lower frequencies (and Finch's high frequency does attract riders), and it'd be a massive infrastructural overkill on a route that is not as affected by traffic as almost any other major arterial route.
Finch may be designated an Avenue between Yonge and Bayview, but the detached houses are being replaced by nothing other than townhouses, so, in fact, Avenueization will result in ever *more* people along that stretch ready to oppose the road widening that would accompany the bus replacement. Finch East has no real Avenues potential and aside from Seneca and the clusters at Warden and McCowan, there isn't anything on Finch, which severely limits future ridership growth and preempts worries about future traffic congestion. In 20-30 years, the population along Finch will either stagnate or go down. Finch East's high ridership is largely a product of people in the area having no other transit options and is already boosted quite a bit by people transferring from N/S routes that take forever to get to the subway.
Speed and capacity can be improved on the 39 by shifting to partial (or more) Rocket service. Transit funding is far, far better spent on extending Sheppard and beefing up non-existent GO service...the Stouffville line doesn't even stop at Finch. The only argument for LRT on Finch East is that it should be well used, but when buses can handle the route, why replace them? There's many other places that need an infrastructural solution to their transit problems. Finch East is not one of them.