When we are moving from left to right in a periodic table that is from La to Lu the size decreases due to increase in nuclear charge. If the size of a central atom decreases in hydroxides the basic character also decreases.
When we compare the basicity of  La(OH)3 & Lu(OH)3 lanthanum hydroxide is more basic

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Basicity depends on size of the cation. The larger the cation, the greater is the basicity. La 3+ in La(OH)3 is larger than Lu 3+ in Lu(OH)3 due to lanthanoid contraction. So La(OH)3 is more basic.
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