This paper studies a $K$-user lattice-code based multiple-access (LCMA) scheme. Each user equipment (UE) encode its message with a practical lattice code, where we suggest a $2^m$-ary \emph{ring code} with symbol-wise bijective mapping to $2^m$-PAM. The coded-modulated signal is spread with its designated signature sequence, and all $K$ UEs transmit simultaneously. The LCMA receiver choose some integer coefficients, computes the associated $K$ streams of \emph{integer linear combinations} (ILCs) of the UEs' messages, and then reconstruct all UEs' messages from these ILC streams. To execute this, we put forth new efficient LCMA \emph{soft detection} algorithms, which calculate the a posteriori probability of the ILC over the lattice. The complexity is of order no greater than $O(K)$, suitable for massive access of a large $K$. The soft detection outputs are forwarded to $K$ ring-code decoders, which employ $2^m$-ary belief propagation to recover the ILC streams. To identify the optimal integer coefficients of the ILCs, a new ``%\emph{bounded independent vectors problem}" (BIVP) is established. We then solve this BIVP by developing a new \emph{rate-constraint sphere decoding} algorithm, significantly outperforming existing LLL and HKZ lattice reduction methods. Then, we develop optimized signature sequences of LCMA using a new target-switching steepest descent algorithm. With our developed algorithms, LCMA is shown to support a significantly higher load of UEs and exhibits dramatically improved error rate performance over state-of-the-art multiple access schemes such as interleave-division multiple-access (IDMA) and sparse-code multiple-access (SCMA). The advances are achieved with just parallel processing and $K$ single-user decoding operations, avoiding the implementation issues of successive interference cancelation and iterative detection.