Alta Verapaz is one of our favorite areas in Guate. We usually drive there so I can't help you with some of the public transport details, but I can give you an overview of the options.
Note that your public transport options for this area are mostly collectivos (public minivans), chicken buses, and tour shuttles. A source for schedules, and other info on the area, is http://www.cobanav.net/info.php. To my knowledge, none of the major bus lines run to Coban except Monja Blanco, and I believe they only run from Guatemala City to Coban.
There are two common routes to Lanquin from Fronteras (Rio Dulce).
One, the route via EL Estor. The roads on this route are mostly unpaved and a bit dicey, sometimes not passable, but this is how the locals typically make the trip.You will find the collectivos on the street in Fronteras. I believe you will catch a collectivo to EL Estor first and then on to Lanquin. If you are an adventuresome traveler then this may be the route for you. I think there are also some tour shuttles which run this route. No major bus lines run this route.
Two, take the main highways (mostly CA-9) to Coban. Paved roads all the way. Even with paved roads wash outs are not uncommon on the last leg to Coban, but they are usually passable, and they have been doing lots of work on this road to improve the situation. This is the route we usually drive, but you can hop collectivos etc to run this route and there are tour shuttles that run it too. From Coban there are many collectivos and tour shuttles which can take you to Lanquin.
Since I usually drive this route I don't have tour shuttle recommendations, but I expect you can find recommendations here on TA.
Always hate to hear of people short-chaning themselves on the Rio Dulce area (I mean the whole Rio not just Fronteras). It is a beautiful place with lots to see and do, but at least it sounds like you are spending some time in Livingston.