Two well-known ASX shares have fallen to fresh 52-week lows on Monday, leaving investors with a decision to make.
Both companies have faced heavy selling pressure, but their longer-term earnings outlooks suggest there could be opportunities at current prices.
So, would I buy either of them today?

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Lynas Rare Earths Ltd (ASX: LYC)
Lynas shares have fallen to a 52-week low of $12.14 on Monday, leaving them down around 40% over the past 12 months.
I think the rare earths producer has an interesting long-term opportunity. Rare earths elements are essential for a range of technologies, including electric vehicles, wind turbines, and defence equipment.
With governments increasingly focused on securing supply chains outside China, Lynas is well-positioned as an established producer and processor of rare earths materials.
The company is also looking to expand its operations. Earlier this month, Lynas announced an agreement to acquire Meteoric Resources Ltd (ASX: MEI), which owns the Caldeira rare earths project in Brazil.
The acquisition could give Lynas access to an important new source of heavy rare earths and support its longer-term expansion plans. But the market does not appear particularly enthusiastic about the deal so far.
Investors may be concerned about the additional investment required to develop Caldeira, the challenges of processing a different type of rare earths resource, and the dilution associated with the all-share acquisition.
I think those concerns are reasonable, although the longer-term earnings outlook remains encouraging. Consensus forecasts point to earnings per share (EPS) of 58.3 cents in FY27, increasing to 92.9 cents in FY28 and $1.13 in FY29.
At $12.14, those estimates put Lynas on approximately 21 times FY27 earnings, falling to just under 11 times FY29 earnings. That could prove cheap if the company delivers the expected growth.
For an investor with a diversified portfolio who wants exposure to the rare earths industry, I think Lynas could be a buy at current levels.
Sonic Healthcare Ltd (ASX: SHL)
Sonic Healthcare shares have also been under pressure, falling to a 52-week low of $18.11 on Monday. That leaves the healthcare company's shares down approximately 18% in 2026.
Sonic operates a global network of pathology and diagnostic businesses, providing essential medical services across several countries.
I like the underlying demand for these services. Ageing populations, advances in medical testing, and the growing importance of early diagnosis should support the industry over time.
But Sonic has some operational challenges to work through. These include improving the performance of its US operations, integrating acquisitions, and managing regulatory and reimbursement changes in certain markets.
I think these issues help explain why investors have become more cautious. Nevertheless, there is some potential for earnings to improve as management makes progress. Consensus forecasts point to EPS of $1.14 in FY27, increasing to $1.26 in FY28 and $1.31 in FY29.
For income investors, the dividend outlook also looks interesting. Analysts expect partially franked dividends of $1.05 per share in FY27, $1.11 in FY28, and $1.14 in FY29.
At $18.11, those forecasts represent potential dividend yields of approximately 5.8%, 6.1%, and 6.3%, respectively.
I think that is a generous level of income, although the relatively high proportion of earnings being paid out leaves limited room for disappointment.
Sonic could therefore be worth considering for patient income investors who are comfortable waiting for the business to improve.
Foolish takeaway
I think both shares deserve a closer look following their recent falls.
For me, Lynas offers the more exciting growth opportunity, although its performance could be unpredictable.
Sonic's potential dividend yield is certainly tempting, but I would want to see more progress on its operational challenges before becoming particularly enthusiastic about the shares.