It doesn't seem to be obvious that /tl/ and /dl/ are especially rare compared to other kinds of stop + liquid onset clusters, so I would be wary of phonological theories or hypotheses that assume or require this to be a fact.
The best discussion that I have found so far is in "KL > TL sound change in Germanic and elsewhere:
Descriptions, explanations, and implications", by Juliette Blevins and Sven Grawunder (2009), which suggests that even though the absence of /tl/ and /dl/ onsets in English (and also in various other IE languages) seems to be a systemic and not just accidental gap, there doesn't seem to be a universal preference against these clusters:
Universal constraints of the form *TL have [...] been proposed, in order to express the crosslinguistically marked status of these clusters and to instantiate
the fact that “homorganic clusters of this kind are avoided in many languages”
(Gouskova 2004: 220). Despite the many analyses of TL gaps, and explanations for their marked status, we are unaware of any typological quantitative
study demonstrating that initial TL clusters are underrepresented in the world’s
languages. In Section 4.2 we offer preliminary typological findings within and
across language families which suggests that they are not.
(§4.1., p. 287 (the page breaks in the linked doc are preliminary, so I don't know whether the published version is slightly different.)
The reference to clusters "of this kind" might be alluding to things like the gaps in English of onset /pw/, /bw/ (not strongly enforced: it could possibly be considered completely accidental, since borrowings like "pueblo" or "bwana" are typically pronounced with /pw/ and /bw/) and /tʃj/, /dʒj/, which can also be seen as being motivated by avoidance of clusters that are in some way overly homorganic.
Some long comments:
"Tl" and "dl" onsets may be analyzed as unitary phonemes rather than clusters. (Actually, I think I remember seing mono-phonemic analyses for even "pl"-type onsets in some language, but I forget which.) This is the usual analysis for Classical Nahuatl: Wikipedia transcribes its "tl" sound as a phoneme /t͡ɬ/. As abarnert's comment and the name of language indicate, this sound can occur word-finally. Wikipedia indicates that Classical Nahuatl is not analyzed as having any complex onsets.
In Indo-European languages, the main context where I am familiar with /tl/ and /dl/ being gaps in the inventory of stop + liquid onsets, there seems to also be a weaker dispreference for clusters like /pl bl kl gl fl/ when compared to /pr br kr gr fr/. Or at least, I have the impression that /pl bl kl gl fl/ are less stable than the obstruent + /r/ clusters. For example, Portuguese historically changed l to r in onset clusters in certain words like branco < Latin blancus, although this is no longer an active change and modern Portuguese does have obstruent + l clusters. Spanish changed /pl kl fl/ to /ʎ/ word-initially and to /tʃ/ after consonants, although again we do see these clusters in modern Spanish as a result of borrowing or dialect mixing. Even though "r" and "l" are both liquids/approximants, I know that in some IE languages such as English, /l/ has been analyzed as being less "sonorous" (in terms of the "sonority hierarchy") than /r/ (the evidence in English for this is stuff like the existence of word-final /rl/, e.g. snarl, but not word-final /lr/).
There are IE languages that have /tl/, or /tl/ and /dl/. Blevins and Grawunder mention Russian, Polish, Serbo-Croatian, Irish, and Pashto (§4.2., (3)), and have more detailed discussion of the different ways languages can get words with these clusters.
Somewhat differently, [tl, dl] are known to be relatively confusable with [kl, gl] for speakers of many IE languages, and apparently there has been a shift of /kl, gl/ to [tl, dl] (unclear to me whether phonemic or just phonetic) in various languages, including dialects of English! (discussed in Blevins and Grawunder)
Although I, like jknappen, am unaware of any consonant cluster inventory databases, I found a paper that mentions various examples of languages with complex syllable structure and that summarizes the types of clusters: "Highly complex syllable structure: a typological study of its phonological characteristics and diachronic
development," by Shelece Easterday (2017).
A brief search for "complex onset" in this document turned up mentions of the following languages that are described as having complex onsets where the second consonant may be /l/:
[gym] NGÄBERE Chibchan, Guaymiic (Panama)
[mji] KIM MUN (VIETNAM DIALECT) Hmong-Mien, Hmong-Mien (Vietnam)
[pac] PACOH Austro-Asiatic, Katuic (Vietnam)
You could check to see whether these or any other of the listed languages have /tl/ or /dl/ clusters.