Both layer packages (.lpk) and layer files (.lyr) are created using ArcGIS Desktop. Layer files store the layer properties, including cartography, and point to the source data. Layer packages encapsulate the data and layer file. Layer packages are ideal for sharing, especially on ArcGIS Online. 

One of the things that the layer file or package author can set is the transparency. There are two lines of thinking when considering transparency in layer file and packages - one approach is that the transparency is set by the author. The other is that no transparency is applied and it's up to the user of the layer file or package to apply transparency if they like. We won't get into a discussion about the merits of the approaches here, but here's how to adjust transparency in Explorer for both scenarios.

In this first example we'll look at a layer package that we've added that has no transparency applied:

We're at maximum opacity, and the layer is completely opaque. To adjust the transparency, just move the slider.

In this second example we've added a layer package with transparency. Though this might seem odd at first, we're at maximum opacity on the slider, but the layer appears somewhat transparent. This makes sense when you consider that what the slider shows is the maximum opacity the author of the layer package chose.

But if we just nudge the slider off of maximum opacity, then we regain control of how the layer looks. Here we've overridden the transparency built-in by the author,and now it's just about completely opaque.

And we can continue to adjust the transparency as we like. Here we're about 70% transparent.

For more information on layers see the Working with ArcGIS Layers and Layer Packages Help topic.

For more information on transparency, see the Controlling Layer Appearance Help topic.