What you need to do is 3 things...
#1 Determine if all the receivers can see both 110 and 119. Since these receivers always stay on the same channel, sometimes they are wired to see only 119, and other times wired only to see 110. If the receivers are connected to a switch to see both satellites, then there is some flexability in moving channels around.
If the some receivers are wired to only see 119, or only see 110, then before you switch channels around you need to make sure the channel your going to change on the receiver is on the satellite its wired for.
Lets say the receiver is on 119 for USA, and you want to switch it to DYI which is on 110, it may not be possible, unless you want to dig into the wiring in the rack and change the satellite input to the other satellite.
#2 Obtain a copy of the bill, and look at the packages. The channel may already be included as part of the package, and it may be as simple as changing a channel on the receiver.
If the reciever can tune in the channel, then its included as part of the package. There would be no way to breach the contract, because the receivers are authorized for all the channels in the package.
For example, you could subscribe to HBO and the receivers would be authorized for all 8 or 9 channels. However since its a headend system, you may only have 1 HBO channel on the system. You could easily add another receiver and modulator and get another HBO channel added to the system at no additional monthly cost. Or you could change one of the channels in the rack to a different channel to add a second HBO channel.
The only thing you cannot mess with is ESPN, as your required to show all the ESPN channels that you pay. For example, there is an ESPN package with 1 channel and an ESPN package with 5 channels. The package with 5 channels is less money then the package with 1 channel, however the contract that Dish has with ESPN is that if you take the discount for the 5 channel package, the headend must show all 5 ESPN channels.
#3 It could be as easy as changing the channel on the receiver, if the programming is part of the package. If not, you need to fill out the add change form and fax it into Dish.
Finally, to ansewer your question LMN is not part of any bulk packages unless they have Top200 as a core programming package which is very unlikely. Its probably too expensive to add Lifetime Movie Network.
It might be possible to add FX, however it will require "The Edge" package which is $.85 per drop. So if there is lets say 100 rooms in this nursing home, then its going to cost an extra $85 per month to have FX.
The tech provider was lying to you when he said it can't be done. This can be added, but does the nursing home want to pay more money per month, if the channels are not included with the package?
If the channels are that important to your mother, she can always get her own Dish account and put a receiver in her room and she can pay a seperate bill under a residential account.