Root objects are sometimes returned for complicated roots of higher degree polynomials.
Sometimes, but no always, ToRadicals can convert Root objects into usually much more complicated nested radicals and get closer to what I think you would consider "ordinary form", but you still have variables in those expressions and that is going to make it more difficult or impossible to get an answer like 3.64.
Unfortunately, after typing your data back in it looks like ToRadicals cannot help you with this one.
All your lambda do appear to even powers. Sometimes you can make a little more progress by substituting z=lambda^2 and working on z instead. Then after you are done you can look at the two square roots of z. Unfortunately this doesn't seem to help in this case either.
All your variables, m, n, a and lambda appear as even powers. Divide all exponents on your variables by 2. If I haven't made any mistakes typing this back in, that gives you a cubic in lambda and reduces the other variable exponents enough that Solve[eqn==0,lambda] is able to recognize it can give you the three roots of the cubic and not use Root objects. Then multiply the exponents on m, n and a by two, find the two square roots of each of those three roots of the cubic and you should have the six roots of your original polynomial in lambda.
But that is still going to leave you with all the m, n and a variables in those six roots.