This seems to be a pretty common scenario in digital marketing, and a few companies have published their approach to lookalike modeling.
Here are a few links:
Maybe you can draw inspiration from what these companies have done. Most of the lookalike systems that I've read about fall into one of the following categories:
segment-approximation models, regression models, and similarity-based models.
Segment-approximation is a similar idea to collaborative filtering. The idea is to find which interests are shared among your seed audience (that is, your past converters). Then you expand the audience by finding new individuals who have a similar interest profile. Obviously this can only be done if you have some information about your potential customers' interests.
Regression models try to compute a membership function which ranges from 0 (not similar to the seed audience at all) to 1 (a member of the seed audience). You use this model to score each potential customer, and those which receive a sufficiently high score are included in the lookalike audience. One challenging aspect of this approach is that you have to use semi-supervised training. You have a set of positive examples (past converters), and you have a much larger pool of mixed-label examples (people who haven't converted).
Similarity-based models generally attempt to learn a useful representation for customers in an unsupervised way. You can then run clustering in the representation space, and your lookalike audience will be those clusters which have high overlap with your seed audience.
Alternatively, you can do similarity comparisons in the representation space, and construct a lookalike audience by thresholding the similarity you find between converters and other potential customers.
The specific learning algorithm that you use will probably vary based on the data you have available. The links above may spark some ideas.
Hope that helps!