No. Socialism gives a constant supply of goods and services, so the less people take care of themselves the more they are rewarded. Distributism gives them a one time chunk of capital. If they don't take care of it, they suffer the consequences. They don't get ongoing services, just the means to take care of themselves.
One's needs are ongoing. A simple one time chunk of capital does not address this. You effectively are arguing for a very healthy lump sum stimulus package, which I'm not quite sure works in most situations. For example, owning a plot of land is useless if you cannot do anything with it. Sure, I have land and I might even have a house, but without the actual means to maintain it, I just have a shelter to live in until my home is foreclosed. I would require a job whose pay allows me to live in the household, which, if I'm getting a random house, is hard to plan for. In effect, you'd be giving me an airplane without the storage space, fuel, parts, or runway to properly utilize it.
In order to achieve the end that everyone gets property, you would need to confiscate non-liquid assets, namely land. In your land example, you would need to forcibly take land owned by private owners (banks), either directly by putting it into government control for the lottery or indirectly by enforcing a law that makes banks hold said lottery. Of course, you would probably construct the lottery to allow for only low-risk people to obtain land, as what is the point of giving land to people who, for whatever reason, will not be able to maintain it. In other words, you'd most likely be giving free land to people who probably bought a house the normal way. Even in the optimal scenario, you'd be giving land to people who on the cusp of being able to afford a house, but can't budget in a mortgage, a group of people I see as rather small in availability for your program, given the requirement to maintain their job and the normal problems of searching for a house.
Also, I think "distributism" is not the correct word for what you want, given what I'm reading from you and what I heard elsewhere. Which is state redistribution of wealth, i.e. socialism. You might want to be more pragmatic than simply offering constant social services to ensure proper incentive to people to work, but this is a question of particular and pragmatic implementation of methodology, not a question of methodology: taking capital from some and redistributing it to others.
