John - given your output, it sounds like you are trying to get the code to do a cumulative sum. If you need to use a for loop, then your calculations need to depend upon the previous iteration.
n = length(lt);
zk = cell(n,1);
zk{1} = lt{1};
for k = 2:n
zk{k} = lt{k} + zk{k-1}; % <--- use previous iteration sum at zk{k-1}
end
