What you can do, is sign up for the free trial, which will let you install the creative cloud cloud app, this in turn will allow you to install LR.
When you cancel your free trial, Lightroom will continue to run, except for the development module - you will not be able to edit your images, you can view them, I suppose you can keep organzing them, but you cannot modify them in LR.
If you want Lightroom, then you have to pay for lightroom
i’ve never had trouble with installation in the nearly 20 years i’ve been using lightroom. you probably should describe what computer and lr version you are using.
lr is subscription only. there is no way to avoid that short of pirating.
In Adobe's best interest, the install is pretty bullet proof. Theoretically @maflynn is correct with after termination the DAM side continues to work but the Develop does not. That makes it a very attractive strategy for those without a catalog full of Lightroom developed images. You get the best DAM available and can continue to develop old and new images in your external editor of choice.
Unfortunately I've never found discussions from those that have actually done the above. Plenty of “this is how Adobe says it will work” but no “this is how it actually did work”. The latter would tell us if a constant bombardment of requests to purchase or sign-ins make the reality an untenable experience.