Not sure if you know how to properly layout the simple lap square, how to use the saw properly, or a framing chisel. There is a technique to using a hand saw to get a nice, square cut. You can leave the blades of the lap slightly long and par with your chisel to sneak up on the final fit to make it a nice tight fit.
First, proper technique to get a square cut is to pick a reference edge, and then a primary and secondary face from that edge. The reference edge should be the edge where the faces are most square. Draw your lines from the primary face across the board/timber, and drop the two short vertical lines. Finally start scoring cuts with the saw along your lines. These will act as guides for your saw. Now saw from top corner until your saw reaches the bottom of one of your dropped vertical lines and the opposite corner (a triangle). Then turn around and do the other corner to corner. Then you can use the kerf to finish the cut and you have a totally square cut. Laying out your lines on hand hewn timber is a bit trickier. You would need to snap chalk lines on your timber to use as references for your square. Since you don't have a straight edge, you need to establish them with chalk lines, but that's a lot to understand right off, so I won't go into it just yet.