Yes, tickets have been scarce since it opened on Broadway over 5 years ago. I have seen it 8 times in various cities and I believe only twice was I able to purchase acceptable seats through the Box Office or Ticketmaster. Other times, I purchased through eBay or a Broker. As a fan, I'm still surprised at the high demand.
You may wish to look at what's offered on eBay, there currently are 70+ auctions for The Lion King on Broadway.
To make it even more of a challenge, I strongly recommend getting Orchesrtra seats only. The inter-active nature of the performance lends itself to Orchestra seating.
Perhaps someone else can suggest an easier way, but myself I have always had to scramble to find tickets for The Lion King.
P.S. Importantly, I've always felt it was worth the effort.
My perfect day would begin at on the beach in Hana, Maui and end at a Broadway Musical.