The situation you describe is ordinary condemnation not inverse condemnation.
If the government is actively taking legal/transactional effort to acquire the lot it is a condemnation.
An inverse condemnation is when the government takes property without court process or trying to pay for it, and you sue for compensation for the property that was taken. If the government just bulldozed a sidewalk in someone's front yard without asking, and the owner sued the government for compensation, that would be an inverse condemnation case.
The short answer is that the government has every right to condemn property adjacent to a highway for use as a sidewalk. This is a classic public purpose.
Generally, the government must first attempt to acquire the property out of court by making an offer for the land, and, if it is unsuccessful in getting the owner to accept its offer, it will bring an eminent domain action to seize the land for public purposes.
In the eminent domain case, the government will win on its right to condemn the land and to take immediate possession of it pending a determination of its value, because the government has the right to seize land to build sidewalks. Then, the rest of the eminent domain case will be over the fair market value of the land taken.