Eva, the answer is it depends (like every legal question)
If the house was fully paid for by LL before his marriage:
The house and any increased equity goes to LL alone.
Any joint funds that were used to improve the house get compensated (like an interest-free loan).
If a mortgage existed on the property:
LL would get his down payment back first, the joint account would get compensate for improvements, and the rest would get divided pro-rata according to the amount of payments made by LL v. the joint account.
For example: $500K house, LL makes a prudent 20% down payment ($100K) for a 30 years fixed loan (no refinancing, it gets messy). LL pays for the house for 5 years and then gets married. LL and wife makes a $50K improvement. Ten years later, LL sadly gets divorced. The house appreciates to $1 million and still has $250K left on the mortgage.
Mortgage gets paid first: $250K
LL gets $100K for his down payment.
Joint account gets $50k for the improvement.
That leaves $600K: LL paid 1/3 of the time while the joint paid the other 2/3. LL would get $200K while joint account gets $400.
LL would get half of the joint account.
In the end, LL would get $300K as separate property and $225K of the account. LL's ex-wife would get $225.
Disclaimer: this is a pure hypothetical and should not be relied upon for any real life situation. Please consult a lawyer before making any legal decisions.
The rest, while compiling, is irrelevant for this particular analysis. LL's potential ex-wife could get spousal support based on Eva's fact pattern.
Of course, it is always better to have things spelled out in writing ahead of time. I am just speaking in generality.
Anyways, all of you now owe me $200.