Lutherans typically do not reserve the Sacrament (some -perhaps many- do).
Lutherans who do not practice reservation of the Sacrament do not refrain from doing so because of any particular doctrine against it, but because they take very seriously Christ’s command to “Take, eat. Take, drink.” Christ doesn’t say anything about “Take, eat some now, and save some for later,” so in typical Lutheran fashion, they don’t put a comma where they understand God to have put a period. Instead, they simply avoid having any leftover altogether. Churches I’ve worshiped at have a simple practice - the elders count how many members are present so no more bread or wine than necessary is consecrated.
If a member is in the hospital or otherwise unable to make it to Divine Service, the pastor typically visits and consecrates the elements on-site, both so as not to subject His Body and Blood to being rather unceremoniously carted around all day as they visit shut-ins (and potentially spilled or dropped!

), and so that the consecration takes place in the presence of the communicant. This is thought to be more in line with Christ’s command, not to mention more pastoral (who doesn’t like a one-on-one visit from their pastor?

).
In short, the traditional Lutheran practice of not reserving the Sacrament is done totally out of reverence for His Body and Blood… If I ever met a person who did not hold such reverence for the Eucharist, yet claimed to be Lutheran, we would have words.
At churches where I’ve worshiped, any remaining Blood in the chalice is either consumed by the pastor or properly disposed, and anything remaining of His Body is either stored separately from the unconsecrated hosts or properly disposed. I know when my father’s congregation (he’s an LCMS pastor) was building a new church a few years ago, members made a particular point to add a piscina, which had been lacking from the original church (a terrible oversight of that hideous 1980’s bunker-church construction!

).
I typically steer clear of Wikis, but this actually explains Lutheran thought fairly well (be sure to read the footnotes, as well):
lutheranwiki.org/How_Long_are_Christ%E2%80%99s_Body_and_Blood_Present_in_the_Consecrated_Bread_and_the_Wine_of_Communion%3F