Table union search (TUS) represents a fundamental operation in data lakes to find tables unionable to the given one. Recent approaches to TUS mainly learn column representations for searching by introducing Pre-trained Language Models (PLMs), especially on columns with linguistic data. However, a significant amount of non-linguistic data, notably represented by domain-specific strings and numerical data in the data lake, are still under-explored in the existing methods. To address this issue, we propose LIFTus, an adaptive multi-aspect column representation for table unionable search, where aspect refers to a concept more flexible than data types, so that a single column can exhibit multiple aspects simultaneously. LIFTus aims at combining different aspects of a column (including both linguistic and non-linguistic aspects) to promote the effectiveness and generalization of TUS in a self-supervised manner. Specifically, besides employing PLMs to extract the linguistic aspects from an individual column, LIFTus trains a pattern encoder to learn possible character-level sequential patterns for the column, and builds a number encoder to capture numerical aspects of the column, including the distribution and magnitude features. LIFTus further utilizes a hierarchical cross-attention aided by aspect-relevant statistics to combine these aspects adaptively in producing the final column representations, which are indexed by vector retrieval techniques to achieve efficient search. Extensive experimental results demonstrate that LIFTus has outperformed the current state-of-the-art methods in terms of effectiveness, and achieved much better generalization capability to support unseen data.