[1a] That lawn will be a bear to maintain.
meets every requirement for a tough construction except that the adjective is replaced by a noun phrase, in this case a bear. Since this is clearly a figurative replacement for an adjective like difficult, let's see if we can classify the sentence as easytough or prettytough.
Can we transpose to a dummy subject? Yup --
[1b] It will be a bear to maintain that lawn.
Can we drop the infinitive? This is a borderline no --
?*[1c] That lawn will be a bear.
If we decide no, then this is an analog to an easytough construction, making the infinitive a complement.
But I say borderline, because the determination might arise from the semantic consideration of mixing the ursine into lawn care. Take the sentence
[2a] The wedding will be a nightmare to attend.
We can still transpose to a dummy subject:
[2b] It will be a nightmare to attend the wedding.
but we can also drop the infinitive:
[2c] The wedding will be a nightmare.
We have a more general statement -- the wedding could be a nightmare to attend or to plan or to pay for -- but it's still grammatical with the same general meaning.
But this problems doesn't arise from a nightmare (or more accurately, a noun like nightmare). Substitute the adjective nightmarish, which sounds more descriptive than evaluative to me. (Although that may be because I have one particular wedding in mind.)
The missing subject is no problem for a tough construction any more than it is for a passive voice construction:
That lawn is maintained with difficulty.
The missing object is a co-referent to the subject, i.e., the lawn, and generative grammarians may pick whatever mechanism allows them to parse the sentence and still sleep at night. The reference to a bear is evaluative, so Boutalt's approach will work for the lawn, unless, of course, we're talking about some strange, two-dimensional topiary. The wedding case may be more of a nightmare.