In both countries, the only way to get a passport is by acquiring citizenship, which requires living in those countries for a continuous period. Thr spouse can't get citizenship ifhe/she isn't living there.
In Lithuania, if the spouse of a citizen lives in the country for seven years as a permanent resident they are eligible to apply for a passport.Getting permanent residency is more or less the same as it is in the US, with registering your foreign marriage with the Lithuanian government, having a place to live, sufficient funds, and so on.
In Poland, the foreign spouse must first live in the country with a temporary residence permit based on marriage. After that, the spouse can apply for permanent residence. The spouse must remain on that status for another year. As long as you haven't been absent for more than 10 months in total over that five year period, the spouse can then apply for citizenship.
One thing that can cause complications in both cases is whether the Lithuanian or Polish citizen was recognized as such at the time of marriage. Lithuanian law doesn't require that a couple be married for any particular period before they apply for citizenship, but Poland says that you have to be married to a citizen for at least three years. Some Polish officials interpret that as meaning that you have to wait for three years after your spouse became a citizen, whilst others counted from the date of your marriage. But under Polish law, once you're recognized as a citizen by right of blood, your citizenship is backdated to the time of your birth. The problem is that not all Polish bureaucrats know that!