I'll try to help shed some light for you. When looking at your 3 Joseph Lucas entries, #1 appears to be in Co. H of the 36th Enrolled Missouri Militia, organized in St. Joseph in August 1862 and serving through Mid November of the same year. This is most likely your veteran from Buchanan County.
#2 is a no show candidate for the St. Louis based 5th EMM in service Sept 1862 to April 1863. By mutal date exclusion these are not likely the same man, not to mention they are clear across the state from one another.
#3 is an entry for the Nodaway County Home Guards that was active July to Sept 1861. Nodaway county is north of Buchanan county by a piece so the geography may be a stretch but certainly not unheard of for members to come from neighboring and near by counties. There is not a time frame exclusion and the NCHG was a large unit fielding 7 companies I believe.
So in summary, #1 is likely your man, but you'd like to have some sort of verification of some sort that does not appear on the SOS info. #2 is not your man. #3 is a maybe and could be the same as #1. Sadly the 36th EMM appears to be bit of a mystery to me, perhaps someone will pipe up with more details on what and who they were. They were in a good place to get their nose bloodied in 1862. The Nodaway Home Guards has better information so you might find something there to help include or exclude #3 as being your guy.
Now that we've got this far, if you spread your search a bit and just search for just last name Lucas in the SOS database you'll get a list that includes a George Lucas. Why is he special? Well he has nearly the exact same entries as your Joseph. First he is listed as a 2nd Lt. Co. D in the Nodaway Home Guards and then shows up one entry later as a 1st Cpl. Co. H in the 36th EMM. Now comes the money stretch... Did Joseph have a relative named George also residing in Buchanan county prior to the war? Could these guys be brothers going to war together? How about father-son?
Now for the icing... Captin of Co D. Nodaway Home Guards was Capt. Robinson, Captain of Co. H 36th EMM was, you guessed it Captain Robinson. Do you start to see the pattern? After a while there gets to be too many commonalities to be just coincidence, so keep on digging and have fun!
Hope this helps.