This takes your basic roll-under attribute check, a discrete skill list, and the basic idea from something like RuneQuest to make a system where every class can advance in skills.
Initial Skills
Take the Lamentations skills, or any other series of skills you want and set them to 0.
Rolling Skills
Any time the referee calls for a skill check roll a d20 under the appropriate attribute (which can change depending on the situation) plus the value in a particular skill.
If you get under this value, you succeed. If not, you fail and place a mark near the skill.
Advancing Skills
When you level up look over your sheet and choose up to three skills to attempt to advance. Roll a d6 and try to roll equal to or over the current skill ranking plus the number of marks next to the skill. If you do so, you advance the skill – improve the skill value by 1.
After you have attempted to advance at least three skills, erase all of the marks.
Justification
This allows anyone to advance in skills, which can be useful if you are not playing with some thief equivalent, or want everyone to be able to learn skills without having to figure out multi-classing.
This also binds the skills to a somewhat reasonable level, making it unlikely for any one in particular to contribute too much over the course of a campaign.