Take a look at the largest venues in the country. Most of them aren't owned by LN, but they still use TM for ticketing. If anything, TM has helped LN to acquire more venues than the other way around. In general, TM has a much more dominant share of the ticketing business than LN has of the venue or promotion business.
Source: I used to own a night club in San Francisco.
"Founded in 1996 by Robert F. X. Sillerman as SFX Entertainment, the company's business was built around consolidating concert promoters into a national entity to counter the oversized influence of ticket behemoth Ticketmaster."
It's kind of amazing how the present distorts our perspective of the past.
The point being: TM already had the market power before LN was on the scene, and all of LN's market power wasn't enough to get people to use their ticketing platform instead of TM. Saying LN is the reason everyone uses TM is very much getting it backwards.
Surely, if LN's dominance is what is needed to lock up the ticketing market, LN's ticketing platform should have been able to compete with TM quite well, and TM should have been struggling to succeed in the ticketing market prior to being acquired by LN.