Lacrosse is a niche sport, primarily played in and dominated by colleges in the Northeast/Mid-Atlantic states, and developed in private high schools in those regions. I know the sport has gradually made its way West, but has done so at the club level, and is not a varsity sport in the most of the rest of the country's high schools or colleges, save a few examples.
I think it is pushed by ESPN because its East Coast execs grew up with it, or have kids playing it, and it is similar to football in excitement and agressive contact, which Americans seem to love. Most US viewers care very little about watching or following the sport, outside of the Northeast/Mid-Atlantic.
Soccer is massively popular, but I think ESPN has a covert antagonistic stance toward American soccer, to preserve the appeal of high school, college, and NFL football, which also occur in the Fall. Over the years, it has become apparent that they have consistently allowed for soccer bashing in virtually every Sports Center broadcast that, despite its rarity, mentions soccer at all. They know the Hispanic and immigrant populations love soccer, so they throw it a bone on occasionally on ESPN2 or over at ESPN Deportes, but this year have even scaled that back, with most MLS games covered on the old OLN/Versus, now NBC Sports channel.
ESPN has an interest in promoting skateboarding to ensure the financial succes of its X Games.